The Lottery data Excel file provides data on the topic of "playing the lottery". It is often claimed that individuals who play the lottery are those who can least afford to do so, making the impact of the lottery "regressive". In this context, regressive implies that lower income individuals play the lottery more than do higher income individuals.

The data for this analysis include 100 randomly chosen men from a major metropolitan area. For each individual, the following information has been recorded:

• The number of times in the preceding month the individual has played a state-sponsored lottery. This is the dependent variable in the accompanying regression analysis.
• The education of the individual, measured by the number of years of schooling completed.Note that 12 years of schooling completed means that the person has graduated from "high school", and 16 years of schooling completed means that the person has graduated from college.
• Age in years at the person's most recent birthday.
• The number of children currently living in the person's household.
• The person's annual "wage and salary" income in the previous year (reported in thousands of dollars).

Use the Excel to address the questions below.

1. Write out the regression equation, with specific intercept and slope estimates.
2. For the first row of actual data only, use the independent variable values to "predict" the value of the dependent variable. For this row, also compute the "residual".
3. For the independent variables "Age" and "Income" interpret the numerical value of the slope.
4. Evaluate the statistical significance of each of the four slope estimates. This can be done in a very summary way. Start out by indicating the "null value" against which you will be testing each of the four slope estimates. Then, next to the name of each independent variable, state whether the slope is "significant", and why. The "why" should be stated in no more than a few words or a single sentence.
5. Is the premise of this research, as stated in the opening paragraph of this question (#3) supported by these regression results? Why or why not (a short answer here is preferable).
6. Interpret the R-square for this regression.

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.658387462			Dep: Lottery
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	Lower 95%	Upper 95%
Intercept	11.90609377	1.785196734	6.669345	1.69E-09	8.362030253	15.45016
Education	-0.43001847	0.132071926	-3.25594	0.001567	-0.69221439	-0.16782
Age	0.029189885	0.025227671	1.157058	0.25015	-0.02089337	0.079273
Children	0.093435096	0.224313376	0.416538	0.677956	-0.35188325	0.538753
Income	-0.07447053	0.027726044	-2.68594	0.008537	-0.12951369	-0.01943

Lottery		Education		Age
Mean	5.39	Mean	12.78	Mean	43.33
Standard Error	0.378699	Standard Error	0.335622	Standard Error	1.198826
Median	6.5	Median	12	Median	42.5
Mode	0	Mode	11	Mode	53
Standard Deviation	3.786993	Standard Deviation	3.356224	Standard Deviation	11.98826
Sample Variance	14.34131	Sample Variance	11.26424	Sample Variance	143.7183
Kurtosis	-1.19235	Kurtosis	-1.05997	Kurtosis	0.543857
Skewness	-0.20308	Skewness	0.199863	Skewness	0.491973
Range	13	Range	13	Range	61
Minimum	0	Minimum	7	Minimum	21
Maximum	13	Maximum	20	Maximum	82
Sum	539	Sum	1278	Sum	4333
Count	100	Count	100	Count	100
Children		Income
Mean	1.78	Mean	32.92
Standard Error	0.132253	Standard Error	1.567001
Median	2	Median	28
Mode	3	Mode	22
Standard Deviation	1.322532	Standard Deviation	15.67001
Sample Variance	1.749091	Sample Variance	245.5491
Kurtosis	-0.00032	Kurtosis	3.412786
Skewness	0.415945	Skewness	1.813328
Range	6	Range	84
Minimum	0	Minimum	11
Maximum	6	Maximum	95
Sum	178	Sum	3292
Count	100	Count	100

Lottery	Education	Age	Children	Income
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