PlanFinan is a financial planning organisation. The data in PlanFinan1.xlsx was obtained from PlanFinan’s database of a particular group of clients. Use Excel to obtain a multiple linear regression of the variable "Home" (Y) on the variables "Salary" (X1) and “Savings” (X2). We want to test whether there is a significant linear relationship between the value of home and the two independent variables. According to the regression output, what is the p-value for the test?

Question

BlackTom AI · Accepted Answer

In this problem, we’re asked to identify the p-value for the test of a significant linear relationship between Home (Y) and the two independent variables Salary (X1) and Savings (X2) using multiple linear regression.
Option a: 6.612E-11. This value could correspond to a t-test or F-test drifting from a different model specification, but it does not match the provided correct answer. It would imply an extremely small p-value, yet our given correct option is smaller in magnitude than this, so this choice is not the one indicated as correct here.
Option b: 1.778E-25. This is the value flagged as correct in the provided data. A p-value on the order of 1.78e-25 indicates an extraordinarily strong overall linear relationship between Home and the two regressors, effectively rejecting the null hypothesis that both coefficients are zero. In the context of multiple regression, this would be the p-value for the test H0: β1 = β2 = 0, against Ha: at least one ≠ 0, usually reported from the ANOVA/F-test associated with the regression model.
Option c: 2.638E-09. While still extremely small and suggestive of significance, this p-value is larger (less significant) than the one indicated as correct. It would correspond to a form of test with a weaker evidence against H0 or a slightly different test statistic, but it does not match the given correct value.
Option d: 1.002E-15. This is another very small p-value, indicating significance, but again it does not match the exact value provided as correct in the data. It could arise from a different model specification or rounding, but it is not the reported p-value here.
To interpret correctly, remember: in multiple regression, the p-value for the overall test of the model (the null that all slopes are zero) is derived from the F-statistic comparing the model with predictors to the reduced model without them. A p-value as small as 1.778e-25 means the observed R^2 is highly unlikely under H0, providing strong evidence of a linear relationship between Home and Salary and Savings.
So, among the given options, the one that matches the stated correct p-value is option b: 1.778E-25.

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