Question

You collect the following information on a sample of 100 adults:

• Y=LOTTERY= percentage of income the person spends on lottery tickets (in %)
• EDUC= amount of education the individual has (in years)
• AGE = age of the individual (in years),
• CHILDREN = number of children the person has (in number of children)
• INC1000= annual income of the individual (in 1,000s of dollars)

The data set can be found in Mod9-1Data. Run the multiple regression in Minitab. Assume a level of significance of 5%.

Lottery	Educ	Age	Children	Inc1000
5	15	50	2	41
7	10	26	0	22
0	13	40	3	24
10	9	46	2	20
5	14	40	3	32
5	15	39	2	42
3	8	36	3	18
0	16	44	1	47
0	20	47	4	85
6	10	52	1	23
0	18	51	2	61
0	17	41	2	70
12	9	42	2	22
7	12	53	1	27
11	9	72	1	25
2	16	38	2	43
11	12	41	5	34
2	14	50	3	53
7	9	41	3	20
0	16	52	0	71
10	9	41	2	16
8	10	45	3	19
1	16	58	0	64
11	11	53	0	25
7	14	61	2	31
3	17	30	1	42
5	17	40	0	50
9	11	73	3	31
5	15	43	4	35
10	9	49	3	18
7	10	50	0	26
10	10	27	1	23
1	17	46	3	39
4	14	47	1	22
7	14	47	3	31
8	12	28	1	29
8	14	26	1	29
3	17	32	2	30
5	16	42	5	21
3	11	53	1	26
0	17	46	1	66
8	14	33	3	29
3	16	52	0	48
8	11	58	3	20
0	18	28	3	80
7	10	53	2	31
7	14	43	1	26
0	16	49	2	36
7	9	38	1	26
9	10	44	0	21
8	9	32	1	24
0	12	44	3	18
7	10	52	0	28
0	16	40	2	42
8	11	53	6	21
7	8	43	2	28
8	17	23	0	27
8	12	21	0	34
7	9	50	3	28
9	12	46	1	30
5	7	82	0	23
0	20	45	3	95
0	11	23	0	22
11	9	40	3	27
8	12	36	3	23
0	10	42	1	29
9	7	36	0	25
7	14	58	3	25
0	16	36	0	28
8	9	37	2	25
6	10	53	2	27
7	17	42	2	39
0	19	50	4	63
8	11	33	0	28
8	11	27	3	29
0	16	30	2	34
7	11	40	2	19
6	13	32	2	22
8	11	69	2	17
0	17	24	0	34
1	17	32	2	44
6	8	21	0	28
0	19	31	2	53
10	11	53	1	16
9	14	43	1	22
5	14	39	1	27
0	7	37	2	22
10	8	57	1	23
10	10	31	1	24
13	8	71	0	11
6	15	59	3	50
7	15	33	3	37
3	11	33	3	24
0	11	41	3	30
5	12	53	3	21
0	16	35	1	53
0	17	54	0	31
10	9	55	2	29
6	16	24	0	36
11	12	56	3	27

null hypothesis for the test on the slope/coefficient on AGE-

alternative hypothesis=

computed test statistic=

table test statistic=

p-value=

statistical conclusion=

Predicted percentage of income spent of lottery tickets for a person with 12 years of education; 20 years old; 0 children; and an income of $25,000.=

null hypothesis for valid regression test=

alternative hypothesis for valid regression=

computed test statistic for the useful regression test=

table test statistic for the valid regression test=

p-value for the valid regression test=

statistical conclusion for the valid regression test=

Answer 1

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.658387462
R Square	0.43347405
Adjusted R Square	0.409620325
Standard Error	2.909780022
Observations	100
ANOVA
	df	SS	MS	F	Significance F
Regression	4	615.442121	153.8605	18.17217	4.09443E-11
Residual	95	804.347879	8.46682
Total	99	1419.79
	Coefficients	Standard Error	t Stat	P-value
Intercept	11.90609377	1.785196734	6.669345	1.69E-09
Educ	-0.430018471	0.132071926	-3.25594	0.001567
Age	0.029189885	0.025227671	1.157058	0.25015
Children	0.093435096	0.224313376	0.416538	0.677956
Inc1000	-0.074470531	0.027726044	-2.68594	0.008537

1. null hypothesis for the test on the slope/coefficient on AGE- H0: β2 = 0

2. alternative hypothesis= H1: β2 ≠ 0

3. computed test statistic= 1.157

4. table test statistic (Using Excel function T.INV.2T(probability,n-2)) = T.INV.2T(0.05,98) = 1.984

5. p-value = 0.250

6. statistical conclusion = Since p-value is more than 0.05, we do not reject null hypothesis and conclude that β2 = 0.

7. Predicted percentage of income spent of lottery tickets for a person with 12 years of education; 20 years old; 0 children; and an income of $25,000.=

y = 11.906 - 0.43*Educ + 0.029*Age + 0.093*Children - 0.074*Inc100

= 11.906 - 0.43*12 + 0.029*20 + 0.093*0 - 0.074*25 = 5.467

8. null hypothesis for valid regression test= H0: β1 = β2 = β3 = β4 = 0

9. alternative hypothesis for valid regression= At least one βi ≠ 0

10. computed test statistic for the useful regression test= 18.172

11. table test statistic for the valid regression test (Using Excel function F.INV(probability,k-1,n-k)) = F.INV(0.05,4-1,100-4) = 0.117

12. p-value for the valid regression test= 0.000

13. statistical conclusion for the valid regression test= Since p-value is less than 0.05, we reject null hypothesis and conclude that at least one βi ≠ 0.