The Following Results Were Obtained from a Multiple Regression Analysis

question 88

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).
Coefficient of determination = 0.7139
a.Write the estimated regression equation for the relationship between the variables.
b.What can you say about the strength of this relationship?
c.Carry out a test of whether y is significantly related to the independent variables. Use a .01 level of significance.
d.Carry out a test of whether x₁ and y are significantly related. Use a .05 level of significance.
e.How many supermarkets are in the sample used here?

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Definitions:

Continuous Reinforcement

A method of learning that involves giving a reward after each desired behavior, promoting the occurrence of the behavior with no delay in reinforcement.

Partial Reinforcement

A conditioning strategy where a response is only occasionally rewarded, leading to stronger and more resistant behaviors.

Immediate Reinforcement

The delivery of a reward or consequence directly following a behavior to strengthen or diminish the recurrence of that behavior.

Delayed Reinforcement

The presentation of a reward or reinforcement after a significant time has passed from the desired behavior, affecting learning and motivation.