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You Have Decided to Analyze the Year-To-Year Variation in Temperature

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You have decided to analyze the year-to-year variation in temperature data.Specifically you want to use this year's temperature to predict next year's temperature for certain cities.As a result,you collect the daily high temperature (Temp)for 100 randomly selected days in a given year for three United States cities: Boston,Chicago,and Los Angeles.You then repeat the exercise for the following year.The regression results are as follows (heteroskedasticity-robust standard errors in parentheses): You have decided to analyze the year-to-year variation in temperature data.Specifically you want to use this year's temperature to predict next year's temperature for certain cities.As a result,you collect the daily high temperature (Temp)for 100 randomly selected days in a given year for three United States cities: Boston,Chicago,and Los Angeles.You then repeat the exercise for the following year.The regression results are as follows (heteroskedasticity-robust standard errors in parentheses): = 18.19 + 0.75 × ;R2 = 0.62,SER = 12.33 (6.46)(0.10) = 2.47 + 0.95 × ;R2 = 0.93,SER = 5.85 (3.98)(0.05) = 37.54 + 0.44 × ;R2 = 0.18,SER = 7.17 (15.33)(0.22) (a)What is the prediction of the above regression for Los Angeles if the temperature in the previous year was 75 degrees? What would be the prediction for Boston? (b)Assume that the previous year's temperature gives accurate predictions,on average,for this year's temperature.What values would you expect in this case for the intercept and slope? Sketch how each of the above regressions behaves compared to this line. (c)After reflecting on the results a bit,you consider the following explanation for the above results.Daily high temperatures on any given date are measured with error in the following sense: for any given day in any of the three cities,say January 28,there is a true underlying seasonal temperature (X),but each year there are different temporary weather patterns (v,w)which result in a temperature different from X.For the two years in your data set,the situation can be described as follows: = X + vt and = X + wt Subtracting from ,you get = + wt - vt.Hence the population parameter for the intercept and slope are zero and one,as expected.Show that the OLS estimator for the slope is inconsistent,where (d)Use the formula above to explain the differences in the results for the three cities.Is your mathematical explanation intuitively plausible? = 18.19 + 0.75 × You have decided to analyze the year-to-year variation in temperature data.Specifically you want to use this year's temperature to predict next year's temperature for certain cities.As a result,you collect the daily high temperature (Temp)for 100 randomly selected days in a given year for three United States cities: Boston,Chicago,and Los Angeles.You then repeat the exercise for the following year.The regression results are as follows (heteroskedasticity-robust standard errors in parentheses): = 18.19 + 0.75 × ;R2 = 0.62,SER = 12.33 (6.46)(0.10) = 2.47 + 0.95 × ;R2 = 0.93,SER = 5.85 (3.98)(0.05) = 37.54 + 0.44 × ;R2 = 0.18,SER = 7.17 (15.33)(0.22) (a)What is the prediction of the above regression for Los Angeles if the temperature in the previous year was 75 degrees? What would be the prediction for Boston? (b)Assume that the previous year's temperature gives accurate predictions,on average,for this year's temperature.What values would you expect in this case for the intercept and slope? Sketch how each of the above regressions behaves compared to this line. (c)After reflecting on the results a bit,you consider the following explanation for the above results.Daily high temperatures on any given date are measured with error in the following sense: for any given day in any of the three cities,say January 28,there is a true underlying seasonal temperature (X),but each year there are different temporary weather patterns (v,w)which result in a temperature different from X.For the two years in your data set,the situation can be described as follows: = X + vt and = X + wt Subtracting from ,you get = + wt - vt.Hence the population parameter for the intercept and slope are zero and one,as expected.Show that the OLS estimator for the slope is inconsistent,where (d)Use the formula above to explain the differences in the results for the three cities.Is your mathematical explanation intuitively plausible? ;R2 = 0.62,SER = 12.33
(6.46)(0.10) You have decided to analyze the year-to-year variation in temperature data.Specifically you want to use this year's temperature to predict next year's temperature for certain cities.As a result,you collect the daily high temperature (Temp)for 100 randomly selected days in a given year for three United States cities: Boston,Chicago,and Los Angeles.You then repeat the exercise for the following year.The regression results are as follows (heteroskedasticity-robust standard errors in parentheses): = 18.19 + 0.75 × ;R2 = 0.62,SER = 12.33 (6.46)(0.10) = 2.47 + 0.95 × ;R2 = 0.93,SER = 5.85 (3.98)(0.05) = 37.54 + 0.44 × ;R2 = 0.18,SER = 7.17 (15.33)(0.22) (a)What is the prediction of the above regression for Los Angeles if the temperature in the previous year was 75 degrees? What would be the prediction for Boston? (b)Assume that the previous year's temperature gives accurate predictions,on average,for this year's temperature.What values would you expect in this case for the intercept and slope? Sketch how each of the above regressions behaves compared to this line. (c)After reflecting on the results a bit,you consider the following explanation for the above results.Daily high temperatures on any given date are measured with error in the following sense: for any given day in any of the three cities,say January 28,there is a true underlying seasonal temperature (X),but each year there are different temporary weather patterns (v,w)which result in a temperature different from X.For the two years in your data set,the situation can be described as follows: = X + vt and = X + wt Subtracting from ,you get = + wt - vt.Hence the population parameter for the intercept and slope are zero and one,as expected.Show that the OLS estimator for the slope is inconsistent,where (d)Use the formula above to explain the differences in the results for the three cities.Is your mathematical explanation intuitively plausible? = 2.47 + 0.95 × You have decided to analyze the year-to-year variation in temperature data.Specifically you want to use this year's temperature to predict next year's temperature for certain cities.As a result,you collect the daily high temperature (Temp)for 100 randomly selected days in a given year for three United States cities: Boston,Chicago,and Los Angeles.You then repeat the exercise for the following year.The regression results are as follows (heteroskedasticity-robust standard errors in parentheses): = 18.19 + 0.75 × ;R2 = 0.62,SER = 12.33 (6.46)(0.10) = 2.47 + 0.95 × ;R2 = 0.93,SER = 5.85 (3.98)(0.05) = 37.54 + 0.44 × ;R2 = 0.18,SER = 7.17 (15.33)(0.22) (a)What is the prediction of the above regression for Los Angeles if the temperature in the previous year was 75 degrees? What would be the prediction for Boston? (b)Assume that the previous year's temperature gives accurate predictions,on average,for this year's temperature.What values would you expect in this case for the intercept and slope? Sketch how each of the above regressions behaves compared to this line. (c)After reflecting on the results a bit,you consider the following explanation for the above results.Daily high temperatures on any given date are measured with error in the following sense: for any given day in any of the three cities,say January 28,there is a true underlying seasonal temperature (X),but each year there are different temporary weather patterns (v,w)which result in a temperature different from X.For the two years in your data set,the situation can be described as follows: = X + vt and = X + wt Subtracting from ,you get = + wt - vt.Hence the population parameter for the intercept and slope are zero and one,as expected.Show that the OLS estimator for the slope is inconsistent,where (d)Use the formula above to explain the differences in the results for the three cities.Is your mathematical explanation intuitively plausible? ;R2 = 0.93,SER = 5.85
(3.98)(0.05) You have decided to analyze the year-to-year variation in temperature data.Specifically you want to use this year's temperature to predict next year's temperature for certain cities.As a result,you collect the daily high temperature (Temp)for 100 randomly selected days in a given year for three United States cities: Boston,Chicago,and Los Angeles.You then repeat the exercise for the following year.The regression results are as follows (heteroskedasticity-robust standard errors in parentheses): = 18.19 + 0.75 × ;R2 = 0.62,SER = 12.33 (6.46)(0.10) = 2.47 + 0.95 × ;R2 = 0.93,SER = 5.85 (3.98)(0.05) = 37.54 + 0.44 × ;R2 = 0.18,SER = 7.17 (15.33)(0.22) (a)What is the prediction of the above regression for Los Angeles if the temperature in the previous year was 75 degrees? What would be the prediction for Boston? (b)Assume that the previous year's temperature gives accurate predictions,on average,for this year's temperature.What values would you expect in this case for the intercept and slope? Sketch how each of the above regressions behaves compared to this line. (c)After reflecting on the results a bit,you consider the following explanation for the above results.Daily high temperatures on any given date are measured with error in the following sense: for any given day in any of the three cities,say January 28,there is a true underlying seasonal temperature (X),but each year there are different temporary weather patterns (v,w)which result in a temperature different from X.For the two years in your data set,the situation can be described as follows: = X + vt and = X + wt Subtracting from ,you get = + wt - vt.Hence the population parameter for the intercept and slope are zero and one,as expected.Show that the OLS estimator for the slope is inconsistent,where (d)Use the formula above to explain the differences in the results for the three cities.Is your mathematical explanation intuitively plausible? = 37.54 + 0.44 × You have decided to analyze the year-to-year variation in temperature data.Specifically you want to use this year's temperature to predict next year's temperature for certain cities.As a result,you collect the daily high temperature (Temp)for 100 randomly selected days in a given year for three United States cities: Boston,Chicago,and Los Angeles.You then repeat the exercise for the following year.The regression results are as follows (heteroskedasticity-robust standard errors in parentheses): = 18.19 + 0.75 × ;R2 = 0.62,SER = 12.33 (6.46)(0.10) = 2.47 + 0.95 × ;R2 = 0.93,SER = 5.85 (3.98)(0.05) = 37.54 + 0.44 × ;R2 = 0.18,SER = 7.17 (15.33)(0.22) (a)What is the prediction of the above regression for Los Angeles if the temperature in the previous year was 75 degrees? What would be the prediction for Boston? (b)Assume that the previous year's temperature gives accurate predictions,on average,for this year's temperature.What values would you expect in this case for the intercept and slope? Sketch how each of the above regressions behaves compared to this line. (c)After reflecting on the results a bit,you consider the following explanation for the above results.Daily high temperatures on any given date are measured with error in the following sense: for any given day in any of the three cities,say January 28,there is a true underlying seasonal temperature (X),but each year there are different temporary weather patterns (v,w)which result in a temperature different from X.For the two years in your data set,the situation can be described as follows: = X + vt and = X + wt Subtracting from ,you get = + wt - vt.Hence the population parameter for the intercept and slope are zero and one,as expected.Show that the OLS estimator for the slope is inconsistent,where (d)Use the formula above to explain the differences in the results for the three cities.Is your mathematical explanation intuitively plausible? ;R2 = 0.18,SER = 7.17
(15.33)(0.22)
(a)What is the prediction of the above regression for Los Angeles if the temperature in the previous year was 75 degrees? What would be the prediction for Boston?
(b)Assume that the previous year's temperature gives accurate predictions,on average,for this year's temperature.What values would you expect in this case for the intercept and slope? Sketch how each of the above regressions behaves compared to this line.
(c)After reflecting on the results a bit,you consider the following explanation for the above results.Daily high temperatures on any given date are measured with error in the following sense: for any given day in any of the three cities,say January 28,there is a true underlying seasonal temperature (X),but each year there are different temporary weather patterns (v,w)which result in a temperature You have decided to analyze the year-to-year variation in temperature data.Specifically you want to use this year's temperature to predict next year's temperature for certain cities.As a result,you collect the daily high temperature (Temp)for 100 randomly selected days in a given year for three United States cities: Boston,Chicago,and Los Angeles.You then repeat the exercise for the following year.The regression results are as follows (heteroskedasticity-robust standard errors in parentheses): = 18.19 + 0.75 × ;R2 = 0.62,SER = 12.33 (6.46)(0.10) = 2.47 + 0.95 × ;R2 = 0.93,SER = 5.85 (3.98)(0.05) = 37.54 + 0.44 × ;R2 = 0.18,SER = 7.17 (15.33)(0.22) (a)What is the prediction of the above regression for Los Angeles if the temperature in the previous year was 75 degrees? What would be the prediction for Boston? (b)Assume that the previous year's temperature gives accurate predictions,on average,for this year's temperature.What values would you expect in this case for the intercept and slope? Sketch how each of the above regressions behaves compared to this line. (c)After reflecting on the results a bit,you consider the following explanation for the above results.Daily high temperatures on any given date are measured with error in the following sense: for any given day in any of the three cities,say January 28,there is a true underlying seasonal temperature (X),but each year there are different temporary weather patterns (v,w)which result in a temperature different from X.For the two years in your data set,the situation can be described as follows: = X + vt and = X + wt Subtracting from ,you get = + wt - vt.Hence the population parameter for the intercept and slope are zero and one,as expected.Show that the OLS estimator for the slope is inconsistent,where (d)Use the formula above to explain the differences in the results for the three cities.Is your mathematical explanation intuitively plausible? different from X.For the two years in your data set,the situation can be described as follows: You have decided to analyze the year-to-year variation in temperature data.Specifically you want to use this year's temperature to predict next year's temperature for certain cities.As a result,you collect the daily high temperature (Temp)for 100 randomly selected days in a given year for three United States cities: Boston,Chicago,and Los Angeles.You then repeat the exercise for the following year.The regression results are as follows (heteroskedasticity-robust standard errors in parentheses): = 18.19 + 0.75 × ;R2 = 0.62,SER = 12.33 (6.46)(0.10) = 2.47 + 0.95 × ;R2 = 0.93,SER = 5.85 (3.98)(0.05) = 37.54 + 0.44 × ;R2 = 0.18,SER = 7.17 (15.33)(0.22) (a)What is the prediction of the above regression for Los Angeles if the temperature in the previous year was 75 degrees? What would be the prediction for Boston? (b)Assume that the previous year's temperature gives accurate predictions,on average,for this year's temperature.What values would you expect in this case for the intercept and slope? Sketch how each of the above regressions behaves compared to this line. (c)After reflecting on the results a bit,you consider the following explanation for the above results.Daily high temperatures on any given date are measured with error in the following sense: for any given day in any of the three cities,say January 28,there is a true underlying seasonal temperature (X),but each year there are different temporary weather patterns (v,w)which result in a temperature different from X.For the two years in your data set,the situation can be described as follows: = X + vt and = X + wt Subtracting from ,you get = + wt - vt.Hence the population parameter for the intercept and slope are zero and one,as expected.Show that the OLS estimator for the slope is inconsistent,where (d)Use the formula above to explain the differences in the results for the three cities.Is your mathematical explanation intuitively plausible? = X + vt and You have decided to analyze the year-to-year variation in temperature data.Specifically you want to use this year's temperature to predict next year's temperature for certain cities.As a result,you collect the daily high temperature (Temp)for 100 randomly selected days in a given year for three United States cities: Boston,Chicago,and Los Angeles.You then repeat the exercise for the following year.The regression results are as follows (heteroskedasticity-robust standard errors in parentheses): = 18.19 + 0.75 × ;R2 = 0.62,SER = 12.33 (6.46)(0.10) = 2.47 + 0.95 × ;R2 = 0.93,SER = 5.85 (3.98)(0.05) = 37.54 + 0.44 × ;R2 = 0.18,SER = 7.17 (15.33)(0.22) (a)What is the prediction of the above regression for Los Angeles if the temperature in the previous year was 75 degrees? What would be the prediction for Boston? (b)Assume that the previous year's temperature gives accurate predictions,on average,for this year's temperature.What values would you expect in this case for the intercept and slope? Sketch how each of the above regressions behaves compared to this line. (c)After reflecting on the results a bit,you consider the following explanation for the above results.Daily high temperatures on any given date are measured with error in the following sense: for any given day in any of the three cities,say January 28,there is a true underlying seasonal temperature (X),but each year there are different temporary weather patterns (v,w)which result in a temperature different from X.For the two years in your data set,the situation can be described as follows: = X + vt and = X + wt Subtracting from ,you get = + wt - vt.Hence the population parameter for the intercept and slope are zero and one,as expected.Show that the OLS estimator for the slope is inconsistent,where (d)Use the formula above to explain the differences in the results for the three cities.Is your mathematical explanation intuitively plausible? = X + wt
Subtracting You have decided to analyze the year-to-year variation in temperature data.Specifically you want to use this year's temperature to predict next year's temperature for certain cities.As a result,you collect the daily high temperature (Temp)for 100 randomly selected days in a given year for three United States cities: Boston,Chicago,and Los Angeles.You then repeat the exercise for the following year.The regression results are as follows (heteroskedasticity-robust standard errors in parentheses): = 18.19 + 0.75 × ;R2 = 0.62,SER = 12.33 (6.46)(0.10) = 2.47 + 0.95 × ;R2 = 0.93,SER = 5.85 (3.98)(0.05) = 37.54 + 0.44 × ;R2 = 0.18,SER = 7.17 (15.33)(0.22) (a)What is the prediction of the above regression for Los Angeles if the temperature in the previous year was 75 degrees? What would be the prediction for Boston? (b)Assume that the previous year's temperature gives accurate predictions,on average,for this year's temperature.What values would you expect in this case for the intercept and slope? Sketch how each of the above regressions behaves compared to this line. (c)After reflecting on the results a bit,you consider the following explanation for the above results.Daily high temperatures on any given date are measured with error in the following sense: for any given day in any of the three cities,say January 28,there is a true underlying seasonal temperature (X),but each year there are different temporary weather patterns (v,w)which result in a temperature different from X.For the two years in your data set,the situation can be described as follows: = X + vt and = X + wt Subtracting from ,you get = + wt - vt.Hence the population parameter for the intercept and slope are zero and one,as expected.Show that the OLS estimator for the slope is inconsistent,where (d)Use the formula above to explain the differences in the results for the three cities.Is your mathematical explanation intuitively plausible? from You have decided to analyze the year-to-year variation in temperature data.Specifically you want to use this year's temperature to predict next year's temperature for certain cities.As a result,you collect the daily high temperature (Temp)for 100 randomly selected days in a given year for three United States cities: Boston,Chicago,and Los Angeles.You then repeat the exercise for the following year.The regression results are as follows (heteroskedasticity-robust standard errors in parentheses): = 18.19 + 0.75 × ;R2 = 0.62,SER = 12.33 (6.46)(0.10) = 2.47 + 0.95 × ;R2 = 0.93,SER = 5.85 (3.98)(0.05) = 37.54 + 0.44 × ;R2 = 0.18,SER = 7.17 (15.33)(0.22) (a)What is the prediction of the above regression for Los Angeles if the temperature in the previous year was 75 degrees? What would be the prediction for Boston? (b)Assume that the previous year's temperature gives accurate predictions,on average,for this year's temperature.What values would you expect in this case for the intercept and slope? Sketch how each of the above regressions behaves compared to this line. (c)After reflecting on the results a bit,you consider the following explanation for the above results.Daily high temperatures on any given date are measured with error in the following sense: for any given day in any of the three cities,say January 28,there is a true underlying seasonal temperature (X),but each year there are different temporary weather patterns (v,w)which result in a temperature different from X.For the two years in your data set,the situation can be described as follows: = X + vt and = X + wt Subtracting from ,you get = + wt - vt.Hence the population parameter for the intercept and slope are zero and one,as expected.Show that the OLS estimator for the slope is inconsistent,where (d)Use the formula above to explain the differences in the results for the three cities.Is your mathematical explanation intuitively plausible? ,you get You have decided to analyze the year-to-year variation in temperature data.Specifically you want to use this year's temperature to predict next year's temperature for certain cities.As a result,you collect the daily high temperature (Temp)for 100 randomly selected days in a given year for three United States cities: Boston,Chicago,and Los Angeles.You then repeat the exercise for the following year.The regression results are as follows (heteroskedasticity-robust standard errors in parentheses): = 18.19 + 0.75 × ;R2 = 0.62,SER = 12.33 (6.46)(0.10) = 2.47 + 0.95 × ;R2 = 0.93,SER = 5.85 (3.98)(0.05) = 37.54 + 0.44 × ;R2 = 0.18,SER = 7.17 (15.33)(0.22) (a)What is the prediction of the above regression for Los Angeles if the temperature in the previous year was 75 degrees? What would be the prediction for Boston? (b)Assume that the previous year's temperature gives accurate predictions,on average,for this year's temperature.What values would you expect in this case for the intercept and slope? Sketch how each of the above regressions behaves compared to this line. (c)After reflecting on the results a bit,you consider the following explanation for the above results.Daily high temperatures on any given date are measured with error in the following sense: for any given day in any of the three cities,say January 28,there is a true underlying seasonal temperature (X),but each year there are different temporary weather patterns (v,w)which result in a temperature different from X.For the two years in your data set,the situation can be described as follows: = X + vt and = X + wt Subtracting from ,you get = + wt - vt.Hence the population parameter for the intercept and slope are zero and one,as expected.Show that the OLS estimator for the slope is inconsistent,where (d)Use the formula above to explain the differences in the results for the three cities.Is your mathematical explanation intuitively plausible? = You have decided to analyze the year-to-year variation in temperature data.Specifically you want to use this year's temperature to predict next year's temperature for certain cities.As a result,you collect the daily high temperature (Temp)for 100 randomly selected days in a given year for three United States cities: Boston,Chicago,and Los Angeles.You then repeat the exercise for the following year.The regression results are as follows (heteroskedasticity-robust standard errors in parentheses): = 18.19 + 0.75 × ;R2 = 0.62,SER = 12.33 (6.46)(0.10) = 2.47 + 0.95 × ;R2 = 0.93,SER = 5.85 (3.98)(0.05) = 37.54 + 0.44 × ;R2 = 0.18,SER = 7.17 (15.33)(0.22) (a)What is the prediction of the above regression for Los Angeles if the temperature in the previous year was 75 degrees? What would be the prediction for Boston? (b)Assume that the previous year's temperature gives accurate predictions,on average,for this year's temperature.What values would you expect in this case for the intercept and slope? Sketch how each of the above regressions behaves compared to this line. (c)After reflecting on the results a bit,you consider the following explanation for the above results.Daily high temperatures on any given date are measured with error in the following sense: for any given day in any of the three cities,say January 28,there is a true underlying seasonal temperature (X),but each year there are different temporary weather patterns (v,w)which result in a temperature different from X.For the two years in your data set,the situation can be described as follows: = X + vt and = X + wt Subtracting from ,you get = + wt - vt.Hence the population parameter for the intercept and slope are zero and one,as expected.Show that the OLS estimator for the slope is inconsistent,where (d)Use the formula above to explain the differences in the results for the three cities.Is your mathematical explanation intuitively plausible? + wt - vt.Hence the population parameter for the intercept and slope are zero and one,as expected.Show that the OLS estimator for the slope is inconsistent,where You have decided to analyze the year-to-year variation in temperature data.Specifically you want to use this year's temperature to predict next year's temperature for certain cities.As a result,you collect the daily high temperature (Temp)for 100 randomly selected days in a given year for three United States cities: Boston,Chicago,and Los Angeles.You then repeat the exercise for the following year.The regression results are as follows (heteroskedasticity-robust standard errors in parentheses): = 18.19 + 0.75 × ;R2 = 0.62,SER = 12.33 (6.46)(0.10) = 2.47 + 0.95 × ;R2 = 0.93,SER = 5.85 (3.98)(0.05) = 37.54 + 0.44 × ;R2 = 0.18,SER = 7.17 (15.33)(0.22) (a)What is the prediction of the above regression for Los Angeles if the temperature in the previous year was 75 degrees? What would be the prediction for Boston? (b)Assume that the previous year's temperature gives accurate predictions,on average,for this year's temperature.What values would you expect in this case for the intercept and slope? Sketch how each of the above regressions behaves compared to this line. (c)After reflecting on the results a bit,you consider the following explanation for the above results.Daily high temperatures on any given date are measured with error in the following sense: for any given day in any of the three cities,say January 28,there is a true underlying seasonal temperature (X),but each year there are different temporary weather patterns (v,w)which result in a temperature different from X.For the two years in your data set,the situation can be described as follows: = X + vt and = X + wt Subtracting from ,you get = + wt - vt.Hence the population parameter for the intercept and slope are zero and one,as expected.Show that the OLS estimator for the slope is inconsistent,where (d)Use the formula above to explain the differences in the results for the three cities.Is your mathematical explanation intuitively plausible? (d)Use the formula above to explain the differences in the results for the three cities.Is your mathematical explanation intuitively plausible?

Definitions:

Permanently Lethargic

Describes a state of continuous tiredness, a lack of energy, and general disinterest in activities, which may stem from various medical or psychological conditions.

Patients

Individuals who receive medical treatment or care from healthcare professionals due to illness or injuries.

Lobotomy

A now-obsolete surgical procedure involving the cutting or scraping away of sections of the frontal lobes of the brain, once used to treat mental illness.

Frontal Lobes

Regions of the cerebral cortex located at the front of the brain, important for voluntary movement, expressive language, and managing higher level executive functions.

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