Question

using spss

2. The following table lists total sales of a specific merchandise in six stores during four seasons (Final Q2.sav): Sales (in thousand dollars) Winter Fall Summer Young Adults Young Adults Young AdultsYoung Adults 57 59 69 60 78 79 68 67 68 67 58 64 65 63 61 63 80 54 63 62 76 68 75 79 64 60 72 81 78 78 83 57 60 58 74 81 78 61 63 61 59 84 57 81 63 (a) Apply an appropriate analysis of variance to this data, justify your choice, and report the complete ANOVA table (must include Source, SS, DF, MS, F, and p). (10 pts) (b) Test the null hypothesis that the sales are the same for all seasons surveyed. (5 pts) (c) Assume that the winter is a control group. Use an appropriate test to compare the control mean sales with the other means, and conclude which season's sales is different from winter. (10 pts) 3. Use the data in the attached file (Final_Q3.sav) with 10 data points of Y and X1, X2, X3, x4, and X5 (a) Fit a simple linear model of Y on one independent variable X2 only, report (1) the Y intercept and regression coefficient; (2) test Ho: B 0. (10 pts) (b) Fit a full linear model of Y on ALL Xs, report (1) the Y intercept and partial regression coefficients; (2) test if there is a significant multiple regression relationship between Y and Xs; (3) test Ho: B3 (for X3). (15 pts) (c) Compare the two models in part (a) and (b), which one do you think fits the data better? Explairn your answer. (5 pts) (d) Analyze and test whether the independent variables X2 and X4 significantly correlated. If the value of X2 increases, how would the value of X4 change? (10 pts)

Answer 1

2)

Q 2)

1) Age (young and adult)

Null hypothesis: The mean sales between the adult and young are the same.

Alternative Hypothesis: The mean sales between the adult and young are not the same.

Season:

Null hypothesis: The mean sales at all the four seasons are the same.

Alternative Hypothesis: At least a season has significantly different mean sales.

Interaction between the Age and Season

Null hypothesis: There is no interaction effect between Age and season on the sales.

Alternative Hypothesis: There is an interaction effect between Age and season on the sales.

a) ANOVA table

Tests of Between-Subjects Effects
Dependent Variable: Sales
Source	Type III Sum of Squares	df	Mean Square	F	Sig.
Corrected Model	2478.979a	7	354.140	12.962	.000
Intercept	219105.188	1	219105.188	8019.711	.000
Age	54.187	1	54.187	1.983	.167
Season	2369.396	3	789.799	28.908	.000
Age * Season	55.396	3	18.465	.676	.572
Error	1092.833	40	27.321
Total	222677.000	48
Corrected Total	3571.813	47

b) The estimated p-value for the season factor is 0.000 and less than 0.05. Hence, we reject the null hypothesis and conclude that at least a season has significantly different mean sales at the 0.05 significance level.

c)

Assuming winter as a control group, the regression analysis is

Predictor	Coef	SE Coef	T	P
Constant	74.917	1.509	49.64	0.000
Spring	-12.083	2.134	-5.66	0.000
Summer	-1.000	2.134	-0.47	0.642
Fall	-16.333	2.134	-7.65	0.000

S = 5.22759 R-Sq = 66.3% R-Sq(adj) = 64.0%

Comment: The estimated p-value for the spring and Fall are less than 0.05. Hence, we can conclude that these two seasons have significant different sales from winter at the 0.05 significance level.