BA 303 - BUSINESS STATISTICS – Weeks 6 & 7: Learning Unit 2: Discussion 2: Chapter 8, Problem 22

BA 303 - BUSINESS STATISTICS – Weeks 6 & 7: Learning Unit 2: Discussion 2: Chapter 8, Problem 22

Use the data in the Excel file Cost of Living Adjustments to find a multiple regression model to predict the salary as a function of all the adjusted cost of living rates. State the model and explain R2, Significance F, and p-values

So,

The model developed should be written as follows:

Salary = 55278.32 + 12020.56*Groceries + 14337.28*Housing + 6711.18*Utilities + 5162.17*Transportation + 12307.68*Healthcare

Predict Salary based upon 10% groceries, 100% housing, -20% utilities, 5% transportation, and 15% healthcare.

Salary = 55278.32 + 12020.56*0.1 +14337.28*1 + 6711.18 (reduce by 20%) +5162.17*0.05 + 12307.68 * 0.15

Salary = $78,290.83

The Adjusted R-squared value is 0.9950 which means that 99.5% of the variation of Salary can be explained by the model parameters.

The Significance-F = 3.83765 E-22 which is < 0.05 which means that the null hypothesis that all the slope coefficients are equal to zero can be rejected and that the model is significant.

The p-value for the coefficient of 'Transportation' is > 0.05 which means we cannot reject the null hypothesis that the slope coefficient of Transportation is zero. So, the value 5162.17 is statistically insignificant at a 5% significance level.

For all other variables, the p-values corresponding to the slope coefficient < 0.05 mean that the null hypothesis that the slope coefficient is zero can be rejected and the respective slope coefficients are significant at a 5% significance level.