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.

Question

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.

Quizplus · Accepted Answer

The Answer of 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.

An Economist Wanted to Analyse the Relationship Between the Speed