The Following Results Were Obtained from a Multiple Regression Analysis $\begin{array} { l l l } & d f & S S \\ \text { Regression } & 2 & 562.363 \\ \text { Residual } & 9 & 225.326 \end{array}$

question 110

Essay

The following results were obtained from a multiple regression analysis of supermarket profitability.The dependent variable, y, is the profit (in thousands of dollars) and the independent variables, x₁ and x₂, are the food sales and nonfood sales (also in thousands of dollars). ANOVA
$\begin{array} { l l l } & d f & S S \\ \text { Regression } & 2 & 562.363 \\ \text { Residual } & 9 & 225.326 \end{array}$
Total ​ $\begin{array}{lcc}& \text { Coefficients } & \text { Standara Error } \\\text { Intercept } & -15.0621 & \\\mathrm{x}_{1} & 0.0972 & 0.054 \\\mathrm{x}_{2}& 0.2484 & 0.092\end{array}$ ​
a.
Write the estimated regression equation for the relationship between the variables.
b.
Compute the multiple coefficient of determination and fully interpret its meaning.
c.
Carry out a test to determine whether y is significantly related to the independent variables. Use a .05 level of significance.
d.
Carry out a test to determine if there is a significant relationship between x₁ and y. Use a .05 level of significance.
e.
How many supermarkets were used in the sample here?

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Definitions:

Interest Rate

The percentage of the principal amount charged by a lender to a borrower for the use of assets, usually expressed as an annual rate.

Down Payment

An initial, upfront payment made for the purchase of an asset, with the balance of the price to be paid later.

Present Value

The valuation today of an incoming stream of cash or one-time future payment, after accounting for a specified rate of return.

Cash Outflows

Money or cash disbursed by the business for various purposes, such as paying expenses, investing in assets, or repaying debts.