A regional retailer would like to determine if the variation in average monthly store sales can, in part, be 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. Complete parts a through c. Use a significance level of 0.10 where needed. 1 Click the icon to view the data table between the store size and average monthly sales. Compute the simple linear regression model using the sample data to determine whether variation in average monthly sales can be explained by store size. What is the linear regression model based on the sample data? y= +( )x (Type integers or decimals rounded to two decimal places as needed.) Interpret the slope coefficient. Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or decimal rounded to two decimal places as needed.) For each additional square foot of store size, the average increase in monthly sales is $._____ For each additional dollar of monthly sales, the average increase in stores size is ____ square feet. Interpret the intercept coefficient. Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or decimal rounded to two decimal places as needed.) The size of a store with average monthly sales of $0 is _______square feet. The average monthly sales of a store with 0 square feet is $ .__________ A store with no floor space cannot occur; therefore, the y intercept does not have a meaningful interpretation. b. Test the significance of the slope coefficient of the regression model. Use a significance level of 0.10. What are the appropriate hypotheses to test? A: H0: 1≤0 HA:1>0 D: H0: 1≠0 HA:1=0 . B: H0: 1<0 HA: 1≥0 E: H0: 1≥0 HA: 1<0 C. H0: 1>0 HA: 1≤0 F. H0: 1=0 HA: 1≠0 Determine the rejection region for the test statistic t. Select the correct choice below and fill in any answer boxes to complete your choice. (Type integers or decimals rounded to three decimal places as needed.) A. t > _____ B. t<_______ or t>__________ C. t< __________ Calculate the simple linear regression test statistic t. t = ______________(Type an integer or decimal rounded to three decimal places as needed.) Since the test statistic (1)___________ in the rejection region, (2)_________ the null hypothesis. Conclude that the regression model (3)__________ significant. This means that knowing x (4)_____- useful help in predicting y. c. Based on the estimated regression model, what percentage of the total variation in average monthly sales can be explained by store size? __________% (Type an integer or decimal rounded to one decimal place as needed.) 1: Data Table of Store Size and Monthly Sales Average Monthly Sales Store Size (Sq. Ft) Average Monthly Sales 17,380 15,820 17,380 17,200 15,890 20,190 15,350 16,880 11,970 12,430 15,570 12,630 21,510 14,160 16,670 14,850 18,350 18,290 16,590 19,960 17,790 $581,933.00 $540,225.00 $638,615.00 $574,536.00 $558,844.00 $692,706.00 $554,571.00 $584,613.00 $474,063.00 $523,828.00 $622,535.00 $468,485.00 $735,274.00 $502,363.00 $627,924.00 $600,644.00 $609,793.00 $613,622.00 $694,818.00 $724,625.00 $535,924.00 1) is not 2) do not reject 3) is 4) does not provide is reject is not provides
A regional retailer would like to determine if the variation in average monthly store sales can, in part, be 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. Complete parts a through c. Use a significance level of 0.10 where needed.
1 Click the icon to view the data table between the store size and average monthly sales.
Compute the simple linear regression model using the sample data to determine whether variation in average monthly sales can be explained by store size. What is the linear regression model based on the sample data?
y= +( )x
(Type integers or decimals rounded to two decimal places as needed.)
Interpret the slope coefficient. Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or decimal rounded to two decimal places as needed.)
-
For each additional square foot of store size, the average increase in monthly sales is $._____
-
For each additional dollar of monthly sales, the average increase in stores size is ____ square feet.
Interpret the intercept coefficient. Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or decimal rounded to two decimal places as needed.)
-
The size of a store with average monthly sales of $0 is _______square feet.
-
The average monthly sales of a store with 0 square feet is $ .__________
-
A store with no floor space cannot occur; therefore, the y intercept does not have a meaningful interpretation.
b. Test the significance of the slope coefficient of the regression model. Use a significance level of 0.10. What are the appropriate hypotheses to test?
A: H0: 1≤0 HA:1>0
D: H0: 1≠0 HA:1=0
.
B: H0: 1<0 HA: 1≥0
E: H0: 1≥0 HA: 1<0
C. H0: 1>0 HA: 1≤0
F. H0: 1=0 HA: 1≠0
Determine the rejection region for the test statistic t. Select the correct choice below and fill in any answer boxes to complete your choice.
(Type integers or decimals rounded to three decimal places as needed.)
A. t > _____
B. t<_______ or t>__________
C. t< __________
Calculate the simple linear regression test statistic t.
t = ______________(Type an integer or decimal rounded to three decimal places as needed.)
Since the test statistic (1)___________ in the rejection region, (2)_________ the null hypothesis. Conclude that
the regression model (3)__________ significant. This means that knowing x (4)_____- useful help in predicting y.
c. Based on the estimated regression model, what percentage of the total variation in average monthly sales can be explained by store size?
__________% (Type an integer or decimal rounded to one decimal place as needed.)
1: Data Table of Store Size and Monthly Sales
Average Monthly Sales
| Store Size (Sq. Ft) | Average Monthly Sales | |
| 17,380 15,820 17,380 17,200 15,890 20,190 15,350 16,880 11,970 12,430 15,570 12,630 21,510 14,160 16,670 14,850 18,350 18,290 16,590 19,960 17,790 |
$581,933.00 $540,225.00 $638,615.00 $574,536.00 $558,844.00 $692,706.00 $554,571.00 $584,613.00 $474,063.00 $523,828.00 $622,535.00 $468,485.00 $735,274.00 $502,363.00 $627,924.00 $600,644.00 $609,793.00 $613,622.00 $694,818.00 $724,625.00 $535,924.00 |
|
1) is not 2) do not reject 3) is 4) does not provide
is reject is not provides
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