An Economist Wanted to Analyse the Relationship Between the Speed

question 110

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:

Defensive Labeling

A strategy employed by companies to preemptively address potential criticisms about their products or services through cautious or mitigative language.

Nonverbal Communication

All elements of communication that do not involve words or language.

Words

Small units of language that convey meaning and can be spoken or written, forming the basis of communication among humans.

Gestures

Movements of the body, especially hands and arms, that convey a message or meaning without using words.