An Economist Wanted to Analyse the Relationship Between the Speed

question 162

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:

Outstanding Checks

Checks that have been written and recorded in the paying entity's cash records but have not yet cleared the bank account.

NSF Check

A check that cannot be processed because the account on which it was drawn lacks sufficient funds, standing for Non-Sufficient Funds.

Outstanding Checks

Checks that have been written and recorded in the payer's ledger but have not yet been cashed or processed by the recipient's bank.

Checks Presented

Refers to the cheques that have been submitted for payment by the payee to the bank but have not yet been cleared.