Question

A national chain of women’s clothing stores with locations in the large shopping malls thinks that it can do a better job of planning more renovations and expansions if it understands what variables impact sales. It plans a small pilot study on stores in 25 different mall locations. The data it collects consist of monthly sales, store size (sq. ft), number of linear feet of window display, number of competitors located in mall, size of the mall (sq. ft),and distance to nearest competitor (ft). USING EXCEL FUNCTIONS

1. Plot the residuals versus the actual values. Do you think that the model does a good job of predicting monthly sales? Why or why not?
2. Do you think that this model will be useful in helping the planners? Why or why not?
3. Test the individual regression coefficients. At the 0.05 level of significance, what are your conclusions?
4. If you were going to drop just one variable from the model, which one would you choose? Why?

Sales	Size	Windows	Competitors	Mall Size	Nearest Competitor
4453	3860	39	12	943700	227
4770	4150	41	15	532500	142
4821	3880	39	15	390500	263
4912	4000	39	13	545500	219
4774	4140	40	10	329600	232
4638	4370	48	14	802600	257
4076	3570	37	16	463300	241
3967	3870	39	16	855200	220
4000	4020	44	21	443000	188
4379	3990	38	16	613400	209
5761	4930	50	15	420300	220
3561	3540	34	15	626700	167
4145	3950	36	14	601500	187
4406	3770	36	12	593000	199
4972	3940	38	11	347100	204
4414	3590	35	10	355900	146
4363	4090	38	13	490100	206
4499	4580	45	16	649200	144
3573	3580	35	18	685900	178
5287	4380	42	15	106200	149
5339	4330	40	10	354900	231
4656	4060	37	11	598700	225
3943	3380	34	16	381800	163
5121	4760	44	17	597900	224
4557	3800	36	14	745300	195

Answer 1

a) Plot of residuals versus the actual values

The residuals "bounce randomly" around the 0 line. This suggests that the assumption that the relationship is linear is reasonable.This also suggests that the variances of the error terms are equal.

Do you think that the model does a good job of predicting monthly sales? Why or why not?

Regression Statistics
Multiple R	0.913723178
R Square	0.834890046
Adjusted R Square	0.791440058
Standard Error	244.883447
Observations	25

Here R-square is 0.8349 which near to 1 indicates our model explains 83.49% information about data. So our fitted model is good for predicting sales.

b)

Do you think that this model will be useful in helping the planners? Why or why not?

Yes the fitted regression model is good because in this model we have 0.8349 which near to 1which indicates model is adquate for prediction purpose with higher accuracy. So for predicting monthly sale one can use this regression model can make the arrangment for future planning about how to increase sales.

c)

Test the individual regression coefficients. At the 0.05 level of significance, what are your conclusions?

	Coefficients	Standard Error	t Stat	P-value
Intercept	1506.801793	672.1868031	2.241641439	0.037118
Size	0.919372513	0.30062727	3.058180697	0.00647
Windows	9.075980803	28.82342842	0.31488207	0.756283
Competitors	-67.68552636	21.95287933	-3.083218622	0.00612
Mall Size	-0.000902855	0.000280615	-3.217412572	0.004534
Nearest Competitor	2.095892895	1.594431056	1.314508324	0.204323

by observing above table

For size p-value = 0.00647 <0.05 so we reject the null hypothesis and conclude that size is significant variable

For Windows p-value = 0.756283 > 0.05 so we accept the null hypothesis and conclude that windows is not significant variable

For Competitors p-value = 0.00612 <0.05 so we reject the null hypothesis and conclude thatCompetitors is significant variable

For Mall Size p-value = 0.004534 <0.05 so we reject the null hypothesis and conclude that Mall Size is significant variable

For Nearest Competitor  p-value = 0.204323 > 0.05 so we accept the null hypothesis and conclude that Nearest Competitor is not significant variable.

d)

we will drop windows variable because For Windows p-value = 0.756283 ( which is highest than remainnig variable)  > 0.05 so we accept the null hypothesis and conclude that windows is not significant variable and statndard error is also high.