A Scatter Plot, Along with the Least Squares Line, of X

question 19

Essay

A scatter plot, along with the least squares line, of x = rainfall volume $\left( \mathrm { m } ^ { 3 } \right)$ and y = runoff volume $\left( \mathrm { m } ^ { 3 } \right)$ for a particular location were given. The accompanying values were read from the plot. $$\begin{array}{l}\begin{array} { l l l l l l l l l } \hline x & 5 & 12 & 14 & 17 & 23 & 30 & 40 & 47 \\\hline y & 4 & 10 & 13 & 15 & 15 & 25 & 27 & 46 \\\hline\end{array}\\\\\begin{array} { c c c c c c c c } \hline x & 55 & 67 & 72 & 81 & 96 & 112 & 127 \\\hline y & 38 & 46 & 53 & 70 & 82 & 99 & 100 \\\hline\end{array}\end{array}$$
a. Does a scatter plot of the data support the use of the simple linear regression model?
b. Calculate point estimates of the slope and intercept of the population regression line.
c. Calculate a point estimate of the true average runoff volume when rainfall volume is 50.
d. Calculate a point estimate of the standard deviation $\sigma$
e. What proportion of the observed variation in runoff volume can be attributed to the simple linear regression relationship between runoff and rainfall?

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Definitions:

Indifference Curve

A graphical representation in microeconomic theory of the combinations of two goods among which a consumer is indifferent.

Midterm Grade

An evaluative score or letter assigned to a student, reflecting their performance halfway through an academic term.

Horizontal Axis

In a graph or chart, the x-axis, representing the independent variable or the basis of comparison across the chart.

Indifference Curves

A graphical representation showing different combinations of two goods among which a consumer is indifferent.