The larger the size of the family the larger the credit balances is for the family. The larger families have the financial needs to have a larger credit balance. 2. Determine the equation of the “best fit” line, which describes the relationship between CREDIT BALANCE and SIZE. Credit Balance ($) = 2591 + 403.2 Size
3. Determine the coefficient of correlation. Interpret.
The square root of R-Squared = .566 equals R; R = .75
4. Determine the coefficient of determination. Interpret. The R-Squared is .566. The R-Squared is stating that 56.6% of the data is correct which indicates that the percentage of the total sample variation of the credit balance value is accounted for by the model.
5. Test the utility of this regression model (use a two tail test with α =.05). Interpret your results, including the p-value. Regression Analysis: Credit Balance ($) versus Size
The regression equation is
Credit Balance ($) = 2591 + 403 Size
Predictor Coef SE Coef T P
Constant 2591.4 195.1 13.29 0.000
Size 403.22 50.95 7.91 0.000
The p-value is 0.000 and therefore less than the α=.05 and we reject the Ho because there was not enough evidence too. 6. Based on your findings in 1-5, what is your opinion about using SIZE to predict CREDIT BALANCE?
The finding that I have from 1-5 that there is a slight positive relationship between the size and credit balance and the reason for this would be because of the prediction of the model for the credit balance to be within 260.162 x2 (520.32) 7. Compute the 95% confidence interval for beta-1 (the population slope). Interpret this interval.
Term Coef SE Coef T P 95% CI Constant 1276.02 273.621 4.66345 0.000 (725.248, 1826.79) Income ($1000) 32.27 4.348 7.42196 0.000 ( 23.520, 41.02) Size 346.85 36.030 9.62668 0.000 (274.327, 419.38) Years 7.88 12.338 0.63885 0.526 (-16.953, 32.72) 8. Using an interval, estimate the average credit balance for customers that have household size of 5. Interpret this interval.
9. Using an interval, predict the credit balance for a customer that has a household size of 5. Interpret this interval.
10. What can we say about the credit balance for a customer that has a household size of 10? Explain your answer.
In an attempt to improve the model, we attempt to do a multiple regression model predicting CREDIT BALANCE based on INCOME, SIZE and YEARS. 11. Using MINITAB run the multiple regression analysis using the variables INCOME, SIZE and YEARS to predict CREDIT BALANCE. State the equation for this multiple regression model. Regression Analysis: Credit Balance ($ versus Income ($1000), Size, Years.
Credit Balance($) = 1276.02 + 32.2719 Income ($1000) + 346.852 Size + 7.88209 Years
12. Perform the Global Test for Utility (F-Test). Explain your conclusion.