A regional retailer would like to determine if the variation in average monthly

Question

A regional retailer would like to determine if the variation in average monthly store sales can, in part explained by the size of the store measured in square feet. A random sample of 21 stores was selected and the store size and average monthly sales were computed A partially completed simple regression table is shown below: Note: additional calculations provided be Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations Ex- 347-520 Ex - 5,879,264,000 40.5139 21 ANOVA MS Regression Residual Total 1,641.3765 113,416.4457 Standard Error 59.8460 r Stat Coefficients 171.2069 0.0253 Intercept a. State the sample regression model? Use any method to test to determine if square feet is a significant variable. Use a level of significance of 0.05 b.

Explanation / Answer

Part a

The sample regression model is given as below:

Y = 0 + 1X

Where, 0 = y-intercept of regression line and 1 = slope for regression line.

We are given

0 = 171.2069

1 = 0.0253

Y = 171.2069 + 0.0253*X

Monthly store sale = 171.2069 + 0.0253*Store size in sq.ft.

Part b

Here, we have to use the t test for coefficient of store size (sq.ft.). The null and alternative hypothesis for this test is given as below:

H0: 1 = 0

Versus

Ha: 1 0

This is a two tailed test.

We are given a level of significance = = 0.05

n = 21

df = n – 1 = 21 – 1 = 20

Test statistic is given as below:

t = 1 / SE(1)

We are given

1 = 0.0253

SE(1) = 0.0036

t = 0.0253/0.0036 = 7.027778

P-value = 0.00

(By using t-table or excel)

P-value < = 0.05

So, we reject the null hypothesis that the variable square feet is not a statistically significant.

There is a sufficient evidence to conclude that square feet is a statistically significant variable.

Part c

The coefficient of determination or the value of R square explains the total variation in the dependent variable due to independent variable.

Formula for coefficient of determination is given as below:

Coefficient of determination = R2 = SSR/SST

We are given,

X = 347520

X^2 = 5879264000

n = 21

Xbar = X/n = 347520/21 = 16548.57143

SSR = 12 * [X^2 – n*Xbar^2]

SSR = 0.0253^2*[5879264000 – 21*16548.57143^2]

SSR = 0.00064009*128304456.1

SSR = 82126.39931

We have

SST = 113416.4457

SSE = SST – SSR

SSE = 113416.4457 - 82126.39931

SSE = 31290.04639

Coefficient of determination = R2 = SSR/SST = 82126.39931/113416.4457 = 0.724113675

This means, about 72.41% of the variation in average monthly sales is explained by store size.

Part d

We are given X = store size = 20000 sq.ft.

Monthly store sale = 171.2069 + 0.0253*Store size in sq.ft.

Monthly store sale = 171.2069 + 0.0253*20000

Monthly store sale = 677.2069

Average estimated monthly store sale = 677.2069

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