a. The estimated regression equation can be written as:
\[y = 653.469 - 53.523(X_1) - 11.028(X_2)\]
Where:
- \(y\) represents the estimated demand for housing.
- \(X_1\) represents the current interest rate (%).
- \(X_2\) represents the rate of unemployment (%).
b. Interpretation of the coefficient values:
- The intercept (653.469): This is the estimated demand for housing when both the interest rate
and unemployment rate are zero. However, in the context of this problem, it may not have a
practical interpretation since interest rates and unemployment rates are unlikely to be zero in
the real world.
- Interest Rate Coefficient (-53.523): This coefficient suggests that for each one-unit increase in
the current interest rate (measured in percentage points), the estimated demand for housing
decreases by approximately 53.523 units, all else being equal. In other words, higher interest
rates are associated with lower demand for housing.
- Unemployment Rate Coefficient (-11.028): This coefficient suggests that for each one-unit
increase in the rate of unemployment (measured in percentage points), the estimated demand
for housing decreases by approximately 11.028 units, all else being equal. This indicates that
higher unemployment rates are associated with lower demand for housing.
c. Comment on the overall strength of the model from the ANOVA table:
The ANOVA table provides information about the overall strength of the model. In this case:
- The Multiple R (correlation coefficient) is 0.923, which is close to 1. This suggests a strong
positive linear relationship between the independent variables (interest rate and
unemployment rate) and the dependent variable (demand for housing).
- The R-squared (R^2) value is 0.852, indicating that approximately 85.2% of the variation in the
demand for housing can be explained by the linear regression model using interest rate and
unemployment rate as predictors. This is a relatively high R-squared value, indicating that the
model does a good job of explaining the variation in housing demand.
- The Adjusted R-squared is 0.754, which is still relatively high and suggests that the model is a
good fit for the data.
d. Comment about the significance of the regression coefficients:
Looking at the significance of the coefficients:
