Final Answer:
(a) The estimated multiple linear regression equation is
.
(b) The t-test results are as follows:
- For Comfort (x₁), the p-value is less than 0.01, rejecting the null hypothesis
. We conclude a significant relationship.
- For Amenities (x₂), the p-value is also less than 0.01, rejecting
, indicating a significant relationship.
- For In-House Dining (x₃), the p-value exceeds 0.01, failing to reject
, suggesting no significant relationship.
(c) Remove the non-significant variable, In-House Dining (x₃), yielding the recommended estimated regression equation:
.
Step-by-step explanation:
In the multiple linear regression equation,
, the coefficients represent the estimated impact of each variable on the overall score. The t-test assesses the significance of each coefficient. For Comfort (x₁) and Amenities (x₂), with p-values less than 0.01, we reject the null hypothesis and infer a significant relationship. However, for In-House Dining (x₃), the p-value exceeds 0.01, suggesting no significant impact.
The removal of non-significant variables simplifies the model. Since the p-value for In-House Dining is not significant, we remove it, resulting in the recommended equation:
. This refined model retains only the significant predictors, enhancing simplicity without sacrificing explanatory power. It ensures a more parsimonious representation of the relationship between the independent variables and the overall score.