A Survey Is Conducted to Determine Whether the Age of Car

question 18

Essay

A survey is conducted to determine whether the age of car influences the annual maintenance cost. A sample of 10 cars is selected and the data is shown below. $$\begin{array} { | c | c | } \hline \text { Age of car (months) } \boldsymbol { x } & \begin{array} { c } \text { Annual Maintenance } \\\text { Cost (\$) } \boldsymbol { y }\end{array} \\\hline 3 & 120 \\\hline 5 & 115 \\\hline 6 & 135 \\\hline 7 & 290 \\\hline 9 & 275 \\\hline 10 & 300 \\\hline 11 & 350 \\\hline 13 & 475 \\\hline 14 & 500 \\\hline 15 & 550 \\\hline\end{array}$$
a. Test whether each of the regression parameters β₀ and β₁ is equal to zero at a 0.05 level of significance.
b. Interpret the estimated regression parameters? Are these interpretations reasonable?

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Definitions:

Personal Income Tax

A tax levied on individuals or households by the government based on their income, with rates typically increasing as income increases.

Federal Personal Income Tax Brackets

Federal Personal Income Tax Brackets are ranges of income taxed at specific rates within the federal tax system, designed to ensure tax is progressively imposed based on earners' ability to pay.

Corporate Income Tax

A tax on the profits made by corporations, affecting their net income and potentially their investment behaviors.

Social Security Tax

A tax levied on both employers and employees to fund the Social Security program, which provides retirement, disability, and survivors' benefits.