Question

For each analysis, write out the null hypothesis, explain what the analysis is looking at, calculate anything you think needs calculating (like expected cell counts), identify whether you think the null is right, and then tell the manager what the results mean.

11. Correlations - I have put the following correlations into a matrix form. Each r is the correlation between the row variable and the column variable. The p value for each r is located immediately below the r.

	Age	$ spent in category	$ spent on our brand	Household size
Age	---	r = .33 p = .05	r = .15 p = .57	r = .18 p = .23
$ Spent in category	r = .33 p = .13	---	r = .48 p = .01	r = .67 p = .01
$ spent on our brand	r = .15 p = .57	r = .48 p = .01	---	r = .04 p = .74
Household size	r = .18 p = .23	r = .67 p = .01	r = .04 p = .74	---

12. Multiple Regression

Source	Variation	F	p
Predicted	735	4.75	.003
Error	4265
Total	5000

Dependent Variable = $ spent on product category

R² = 735/5000 = 14.7%

	b	Beta	p
Household size	3.5	.245	.02
Household Income	257.83	.475	.005

13. Multiple Regression

Source	Variation	F	p
Predicted	132	2.32	.34
Error	3155
Total	3287

Dependent Variable = $ spent on product category

R² = ?

	b	Beta	p
Commuting Distance	.356	.044	.974
Value of Home	1.83	.0052	.835

14. Multiple Regression

Source	Variation	F	p
Predicted	575	12.87	.01
Error	2000
Total	2575

Dependent Variable = $ spent on product category

R² = ?

	b	Beta	p
Hours spent on recreation	5.75	.762	.000
Hours spent listening to music	8.66	.003	.961

15. Multifactor ANOVA A = type of ad; B = price level

Source	Variation	F	p
Main Effect (A)	27.5	2.11	.24
Main Effect (B)	58.9	6.75	.03
A x B Interaction	45.7	4.98	.05
Within	325
Total	457.1

Dependent Variable = Purchase Intention

Means

	Ad 1	Ad 2
Price 1	7.5	3.5
Price 2	4.0	8.2

Answer 1

if p value < 0.05, there is correlation between two variables

p value >0.05 no correlation

12)

p = 0.003

conclusion :    p-value<α , reject null hypothesis

Model is significant.

Both Household size and Household Income have less p value means both variable are significant in model.

13)

p value =0.34

p value > 0.05

not significant

so, not a good modal

also, commuting distance and value of home are not significant , we find that the fitted model is not significant. The goodness of fit of the model can be determined using the Coefficient of Determination measure R² which gives the proportion of explained variation in the model:

%

We find that the predictors in the model could explain only about 4% variation in $ spent on product category. This supports the conclusion that the fitted model is not significant and the model cannot be used effectively for predicting the amount spent.

Looking at the fitted regression equation,

Predicted $ spent on product category = 0.044 ( Commuting Distance ) + 0.0052 ( Value of Home )

We find that both the estimated slope coefficients 0.044 (p-value = 0.974> 0.05) and 0.0052 (p-value = 0.835 > 0.05) fail to contribute significantly in predicting the $ spent on product category.

14.

Here, using Multiple regression, we may establish a causal relationship between the probable predictors and the dependent variable - $ spent on product category (at say, 5% level of significance). Looking at the test results, F = 12.87, p-value = 0.01 < 0.05, we find that the fitted model is significant at 5% level. The goodness of fit of the model can be determined using the Coefficient of Determination measure R2 which gives the proportion of explained variation in the model:

%

We find that the predictors in the model explain about 22.3% variation in $ spent on product category. Looking at the fitted regression equation,

Predicted $ spent on product category = 0.762 ( Hours spent on recreation ) + 0.003 ( Hours spent listening to music )

We find that the estimated slope coefficient of Hours spent on recreation, 0.762 (p-value = 0.000 < 0.05) contribute significantly in predicting the $ spent on product category but not Hours spent listening to music, 0.0052 (p-value = 0.961 > 0.05).

Although this model is significant, since this explains only 22.3% variation, rerunning the model by eliminating the insignificant predictor (Hours spent listening to music) we might get a more efficient model.

MULTI-FACTOR ANOVA:

We test:

Factor A has no effect on a significant effect on Purchase Intention Factor A has not effect on Purchase Intention    There is no interaction between factors A and B

Vs

Factor A has a significant effect on Purchase Intention    Factor A has a significant effect on Purchase Intention    There is a interaction between factors A and B

From the F test of overall significance obtained from ANOVA table, we find that effect of Factor B (F = 6.75, p-value = 0.03) and Interaction AB (F = 4.98, p-value = 0.05) on Purchase Intention is significant at 5% level.  

Multi factor ANOVA A = type of ad; B = price level

Main Effect (A)	27.5	2.11	.24	p value > α , Insignificant
Main Effect (B)	58.9	6.75	.03	p value < α , significant
A x B Interaction	45.7	4.98	.05	p value = α , insignificant

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