Question

In: Statistics and Probability

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 2
8803 53 13 1
9571 52 15 2
9566 77 12 3
7885 32 14 3
9773 55 11 1
9121 52 15 2
9298 43 14 3
10285 65 15 2
7801 38 12 1
9323 52 14 2
8643 36 16 3
12466 85 15 2
9447 64 14 2
10727 86 15 2
9243 57 15 3
9311 68 12 2
11033 74 14 3
11721 82 16 2
8727 24 15 3
8438 37 15 3
8317 55 12 2
8617 50 14 1
9052 39 16 3
10889 73 15 3
7766 26 14 1
9189 47 15 2
  1. Use data in BUSI1013 Credit Card Balance.xlsx to complete the following. You will need to use a statistical package such as StatTools or the Regression program within Excel’s Data Analysis Add-in to generate the estimated regression equation and the ANOVA etc. (12 points)
    1. 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?
    2. Comment on the goodness of fit of the model using the coefficient of determination.
    3. Conduct an F test with the critical value approach to see whether the overall model is significant. Use α = 0.01.
    4. Perform a t test with p-value approach for the significance of the Income variable. Use α = 0.05.
    5. Perform a t test with the p-value approach for the significance of the Size of Household variable. Use α = 0.05.
    6. 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:

Following is the output of regression anaysis generated by excel:

The multiple regression equation is

(b)

The coefficient of determination is

It shows that 77.2% of variation in accoutn balance is explained by model that is by the independent variables Income, Years of Education, Size of Household.

(c)

The F test statistics is

F = 45.10

The critical value of F using excel function "=FINV(0.01,3,40)" is

Since so we can conclude that model is significant.

(d)

The test statistics for income variable is

t = 10.186

The p-value is

p-value = 0.0000

Since p-value is less than α = 0.05 so income variable is significant to the model.

(e)

The test statistics for Size of Household variable is

t = 1.707

The p-value is

p-value = 0.0956

Since p-value is greater than α = 0.05 so Size of Household variable is not significant to the model.

(f)

The estimated account balance is

orchestra answered 2 years ago
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