Question

(1 point) A national sporting good store wishes to use demographic information to predict its monthly sales, in $1000s. Thrity-eight, n=38n=38, stores of the chain are randomly chosen across the country. It is known that each store is approximately the same size and carries the same merchandise.

The geographic area from which a store draws its customers is known as the customer base. One of the variables is the percentage of the customer 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 in store ii customer base that have graduated from high school

A least-squares regression was ran in R producing the following output:



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 the slope 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 sales cannot be explained by its linear dependency on the percentage of the customer base that are high school graduates? Enter your answer as a percentage, using two decimal places.

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%


(c) Does the data collected indicate that the monthly sales of a store can be expressed as a linear function the percentage of high school graduates in its customer base? Select the correct statisticaly 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 determined in (c). Find the value of the test statistic, using two decimals in your answer.

FcalcFcalc =

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(e) Testing the statistical hypotheses in (c) at α=0.05α=0.05, you can conclude from this data that the  ? monthly sales of a store percentage of customer base that are high school graduates   ? can cannot  be expressed as a linear function of the  ? monthly sales of a store percentage of customer base that are high school graduates .


(f) Can you infer from this data that an increase of 1% to the percentage of high school graduates in the customer based will lead to an mean/average increase in the store's monthly sales by more than $50,000?


(i) Find the value of the test statistic, use two decimal places in your 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 that 90% of its customer base has a high school diploma. With 95% confidence, estimate this store's monthly sales for the current month.
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 the model? Pick the most appropriate answer.

A. The variance in the monthly sales is not the same for all stores with different proportions of high school graduates in their respective customer base.
B. The variance in the monthly sales is the same for all stores with different proportions of high school graduates in their respective customer base.
C. The distribution in the monthly sales is Normally distributed.
D. The distribution in the monthly sales is not Normally distributed.
E. The variation in the proportion of the customer base that are high school graduates is the same for all stores.
F. The variation in the proportion of the customer based that are high school graduates is not the same for all stores.

COULD YOU ANSWER ONLY ON QUESTION H, G, E, F

Answer 1