(1 point) A national sporting good store wishes to usedemographic information to predict its monthly sales, in $1000s.Thrity-eight, n=38n=38, stores of the chain are randomly chosenacross the country. It is known that each store is approximatelythe same size and carries the same merchandise.
The geographic area from which a store draws its customers is knownas the customer base. One of the variables is the percentage of thecustomer base who have graduated from high school.
MonthlySalesiMonthlySalesi = β0β0 +β1PercentHSGradsiβ1PercentHSGradsi + eiei
where
MonthlySalesiMonthlySalesi - is the total sales in month ii, in$1000s
PercentHSGradsiPercentHSGradsi - is percentage of all customers instore ii customer base that have graduated from high school
A least-squares regression was ran in R producing the followingoutput:
Regression Analysis: MonthlySales versus PercentHSGrads
| Predictor | Coef | SD Coef | T | P |
| Constant | -2970 | 1371 | | |
| PercentHSGrads | 59.66 | 17.67 | | |
S = 802.004 R-Sq =
| Analysis of Variance | | | | | |
| Source | DF | SS | MS | F | P |
| Regression | | 7333350 | | | |
| Residual Error | | 23155564 | | | |
| Total | 37 | | | | |
Using the partial R output, answer the questions below.
(a) Estimate the model. Use two-decimals your estimation of theslope term, no decimals in the estimation of the y-intercept.
MonthlySalesiˆMonthlySalesi^ =
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+
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PercentHSGradsiPercentHSGradsi
(b) What percentage of the variation in a store's monthly salescannot be explained by its linear dependency on the percentage ofthe customer base that are high school graduates? Enter your answeras a percentage, using two decimal places.
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%
(c) Does the data collected indicate that the monthly sales of astore can be expressed as a linear function the percentage of highschool graduates in its customer base? Select the correctstatisticaly hypotheses.
A. H0:βˆ1≥0HA:βˆ1<0H0:β^1≥0HA:β^1<0
B. H0:β1=0HA:β1≠0H0:β1=0HA:β1≠0
C. H0:β1=0HA:β1<0H0:β1=0HA:β1<0
D. H0:βˆ1≥0HA:βˆ1≠0H0:β^1≥0HA:β^1≠0
E. H0:β1≥0HA:β1>0H0:β1≥0HA:β1>0
F. H0:βˆ1=0HA:βˆ1>0H0:β^1=0HA:β^1>0
(d) Using the FF-test, test the statistical hypotheses determinedin (c). Find the value of the test statistic, using two decimals inyour answer.
FcalcFcalc =
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(e) Testing the statistical hypotheses in (c) at α=0.05α=0.05, youcan conclude from this data that the  ? monthly sales ofa store percentage of customer base that are high schoolgraduates   ? can cannot  be expressed asa linear function of the  ? monthly sales of a storepercentage of customer base that are high school graduates .
(f) Can you infer from this data that an increase of 1% to thepercentage of high school graduates in the customer based will leadto an mean/average increase in the store's monthly sales by morethan $50,000?
(i) Find the value of the test statistic, use two decimal places inyour answer.
TcalcTcalc =
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(ii) Find the PP-value of the result, using three decimals.
PP-value =
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(g) A store located at a local mall has recently discovered that90% of its customer base has a high school diploma. With 95%confidence, estimate this store's monthly sales for the currentmonth.
Note: You will need∑38i=1PercentHSGradsi=2935.17∑i=138PercentHSGradsi=2935.17 and∑38i=1PercentHSGrads2i=228777∑i=138PercentHSGradsi2=228777
Lower Bound =
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$1000s (use one decimal in your answer)
Upper Bound =
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$1000s (use one decimal in your answer)
(h) A residual plot of the regression was consulted.
What does this residual plot say about the condition(s) of themodel? Pick the most appropriate answer.
A. The variance in the monthly sales is not thesame for all stores with different proportions of high schoolgraduates in their respective customer base.
B. The variance in the monthly sales is the samefor all stores with different proportions of high school graduatesin their respective customer base.
C. The distribution in the monthly sales isNormally distributed.
D. The distribution in the monthly sales is notNormally distributed.
E. The variation in the proportion of the customerbase that are high school graduates is the same for allstores.
F. The variation in the proportion of the customerbased that are high school graduates is not the same for allstores.
COULD YOU ANSWER ONLY ON QUESTION H, G, E, F
