Answered step by step
Verified Expert Solution
Link Copied!

Question

1 Approved Answer

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

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

Step by Step Solution

There are 3 Steps involved in it

Step: 1

blur-text-image

Get Instant Access to Expert-Tailored Solutions

See step-by-step solutions with expert insights and AI powered tools for academic success

Step: 2

blur-text-image

Step: 3

blur-text-image

Ace Your Homework with AI

Get the answers you need in no time with our AI-driven, step-by-step assistance

Get Started

Recommended Textbook for

WebAssign For A First Course In Differential Equations With Modeling Applications

Authors: Dennis G Zill

11th Edition

1337879770, 9781337879774

More Books

Students also viewed these Mathematics questions

Question

=+a) Create a run chart for the baseballs circumferences.

Answered: 1 week ago