An Economist Wanted to Analyse the Relationship Between the Speed

question 113

Essay

An economist wanted to analyse the relationship between the speed of a car (x) in kilometres per hour (kmph) and its fuel consumption (y) in kilometres per litre (kmpl). In an experiment, a car was operated at several different speeds and for each speed the fuel consumption was measured. The data obtained are shown below. $$\begin{array} { | l | l | l | l | l | l | l | l | } \hline \text { Speed (mph) } & 25 & 35 & 45 & 50 & 60 & 65 & 70 \\\hline \begin{array} { l } \text { Fuel consumtion } \\\text { (mpg) }\end{array} & 40 & 39 & 37 & 33 & 30 & 27 & 25 \\\hline\end{array}$$ a. Find the least squares regression line.
b. Calculate the standard error of estimate, and describe what this statistic tells you about the regression line.
c. Do these data provide sufficient evidence at the 5% significance level to infer that a linear relationship exists between higher speeds and lower fuel consumption?
d. Predict with 99% confidence the fuel consumption of a car traveling at 55 kmph.

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Definitions:

Social Constructions

Theories or concepts that suggest that the realities of the world are not inherent, but are constructed by social processes, shaped by cultural and historical contexts.

Social Stratification

The division of society into different hierarchically arranged levels based on factors like wealth, power, race, or education.

Achieved Status

Attributes developed throughout life as a result of effort and skill (e.g., course grades).

Biological Superiority

A controversial concept suggesting that some races or species are inherently superior to others based on biological differences.