Question
In: Statistics and Probability
What is the estimated regression equation using Account Balance as the dependent variable, and Income, Years of Education, as well as Size of Household as the independent variable?
| Regression Statistics | ||||
| Multiple R | 0.878541582 | |||
| R Square | 0.771835311 | |||
| Adjusted R Square | 0.75472296 | |||
| Standard Error | 552.6878046 | |||
| Observations | 44 | |||
| ANOVA | ||||
| df | SS | MS | F | |
| Regression | 3 | 41332908 | 13777636 | 45.10399 |
| Residual | 40 | 12218552 | 305463.8 | |
| Total | 43 | 53551461 | ||
| Coefficients | Standard Error | t Stat | P-value | |
| Intercept | 2095.365223 | 841.1044 | 2.491207 | 0.016979 |
| Income | 51.95408819 | 5.100341 | 10.1864 | 0.00 |
| Years of Education | 288.9485028 | 56.13512 | 5.147375 | 0.00 |
| Size of Household | 207.4655622 | 121.5576 | 1.706727 | 0.095626 |
- What is the estimated regression equation using Account Balance as the dependent variable, and Income, Years of Education, as well as Size of Household as the independent variable?
b. Comment on the goodness of fit of the model using the coefficient of determination.
c. Conduct an F test with the critical value approach to see whether the overall model is significant. Use α = 0.01.
d. Perform a t test with p-value approach for the significance of the Income variable. Use α = 0.05.
e. Perform a t test with the p-value approach for the significance of the Size of Household variable. Use α = 0.05.
f. Estimate the Account Balance of a customer who has an income of $62 thousand, 14 years of education, and a household size of 3.
Solutions
Expert Solution
a). Regression equation:
b) Coefficient of determination, R2 = 0.7718
adjusted R2 = 0.7547
Around 75.47% of the variability of Account balance can be explained by the linear relationship.
It is a good fit.
c) Test statistic, F = 45.10399
p-value = F.DIST.RT(45.10399, 3, 40) = 0.00
As p-value = 0 <0.01, we reject the null hypothesis.
The model is significant.
d) T-test for income variable, t = 10.1864
and p-value = 0.00
As p-value = 0 < 0.05, we reject the null hypothesis.
The independent variable income is significant.
e) T-test for Size of Household variable, t =1.706727
and p-value = 0.0956
As p-value = 0.0956 > 0.05, we fail to reject the null hypothesis.
The independent variable income is not significant.
f) Estimated Account Balance of a customer who has an income of $62 thousand, 14 years of education, and a household size of 3.
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Size
Amount
Charged ($)
54
3
4,016
30
2
3,159
32
4
5,100
50
5
4,742
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2
1,864
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2
4,070
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Income
($1000s)
Household
Size
Amount
Charged ($)
54
3
4,016
30
2
3,159
32
4
5,100
50
5
4,742
31
2
1,864
55
2
4,070
37
1
2,731
40
2
3,348
66
4
4,764
51
3
4,110
25
3
4,208
48
4
4,219
27...
Develop estimated regression equations, first using annual income as the independent variable and then using household...
Develop estimated regression equations, first using annual
income as the independent variable and then using household size as
the independent variable. Which variable is the better predictor of
annual credit card charges? Discuss your findings -
Income
($1000s)
Household
Size
Amount
Charged ($)
54
3
4,016
30
2
3,159
32
4
5,100
50
5
4,742
31
2
1,864
55
2
4,070
37
1
2,731
40
2
3,348
66
4
4,764
51
3
4,110
25
3
4,208
48
4
4,219
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Account Balance Income Years of Education Size of Household 8976 63 12 2 8308 37 14...
Account Balance
Income
Years of Education
Size of Household
8976
63
12
2
8308
37
14
2
10028
52
16
2
11256
64
15
4
9869
47
17
2
10194
74
15
2
8706
49
12
2
9557
58
14
2
10565
70
16
3
9434
69
11
3
9687
25
18
3
9490
57
15
1
8806
46
14
3
9561
48
16
2
11757
80
15
3
9406
66
14
2
11150
46
15
3
7671
28
12...
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Income
Years of Education
Size of Household
8976
63
12
2
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37
14
2
10028
52
16
2
11256
64
15
4
9869
47
17
2
10194
74
15
2
8706
49
12
2
9557
58
14
2
10565
70
16
3
9434
69
11
3
9687
25
18
3
9490
57
15
1
8806
46
14
3
9561
48
16
2
11757
80
15
3
9406
66
14
2
11150
46
15
3
7671
28
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