The Following Results Were Obtained from a Multiple Regression Analysis

question 107

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
DF SS
Regression 2 562.363
Residual 9 225.326
Total
$\begin{array}{lr}&\text { Coefilicient }&\text { Standard Error }\\\text { Intercept } & -15.0621 \\X_{1} & 0.0972&0.054 \\X_{2} & 0.2484&0.092\end{array}$
a. Write the estimated regression equation for the relationship between the variables.
b. Compute the coefficient of determination and fully interpret its meaning.
c. Carry out a test of whether Y is significantly related to the independent variables. Use a 0.05 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 in the sample used here?

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Definitions:

Unitary Elasticity

A situation in which the percentage change in quantity demanded or supplied is equal to the percentage change in price.

Percentage Increase

A measurement that calculates the degree to which a value has risen compared to its previous value, expressed as a percentage.

Price Elasticity

Measures how much the quantity demanded of a good changes in response to a change in its price.

Coefficient

A numerical or constant quantity placed before and multiplying the variable in an algebraic expression.