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:

Physiologically Aroused

A state in which the body's physiological functions are heightened, such as increased heart rate or adrenaline, often in response to stress or excitement.

Cultures of Honor

Societal norms that value honor and personal reputation, often responding to insults or threats aggressively to maintain status.

Status and Reputations

The recognition and esteem individuals or groups hold within a society, often reflecting their social standing, achievements, or character.

Culture of Honor

A societal norm that emphasizes the defense of one's reputation or honor through toughness and aggression.