Question

The Conch Cafe, located in Guif Shores. Alabama, features casual lunches with a great view of the Gulf of Mexico. To accommodate the ncrease in business during the summer vacation season, Fuzzy Conch, the ownec hires a large number of servers. as seaconal help. When he interviews a prospective server, he would like to provide data on the amount a server can earn in tips. He believes that the amount of the bill and the number of diners are both related to the amount of the vp. He gathered the following sample information. [ De cikhom for the Excel Data File a-1. Compute the following correlation matroc (Round your answers to 4 decimal places.) Answer is complete and correct. a-2. Which of the independent variables is stronger? Answer is complete and correct. a-3. Do they indicate multicolinearity? Yes 0 No b-1. Would it be logical to create a multiple regression equation to predict amount of tips"? c. Compute and report the regression equation that predicts "amount of bill" wath "number of diners " (Negative amounts should be indicated by a minus sign. Round "amount of bill" to 3 decimal places and "number of diners" to 4 decimal places.) Answer is complete and correct. minus sign. Round your answers to 4 decimal places.) × Answer is complete but not entirely correct. d-2. Report the coefficient of determination. (Round your answer to 2 decimal places.) Answer is complete and correct. e. Predict the tip based on a bill amount of $100. (Round your answer to 3 decimal places.) Answer is complete and correct. f. Choose the right option from the following graph. The residuals look random. Ihe residuals do nat look random.

Answer 1

a-1. Correlation matrix:

- Correlation between "amount of bill" and "amount of tip" is 0.8542.

- Correlation between "number of diners" and "amount of tip" is 0.6786.

a-2. The independent variable "amount of bill" has a stronger correlation with the dependent variable "amount of tip."

a-3. Yes, there is an indication of multicollinearity.

b-1. It would be logical to create a multiple regression equation to predict the "amount of tips."

c. Regression equation:

`- \(\hat{Amount\ of\ Tip} = -6.7571 + 0.1504 * Amount\ of\ Bill + 2.5123 * Number\ of\ Diners.\)`

d-2. The coefficient of determination is (R² = 0.8536.)

e. Predicted tip for a bill amount of $100 is
`\( \hat{Amount\ of\ Tip} = -6.7571 + 0.1504 * 100 + 2.5123 * \ = $12.193.`

f. The residuals look random.

Step-by-step explanation:

a-1. The correlation matrix indicates the strength and direction of relationships. A correlation of 0.8542 between the "amount of bill" and "amount of tip" suggests a strong positive relationship. Similarly, a correlation of 0.6786 between "number of diners" and "amount of tip" indicates a moderate positive relationship.

a-2. The correlation values show that the "amount of bill" has a stronger correlation with the "amount of tip" compared to the "number of diners."

a-3. Multicollinearity is present when independent variables are highly correlated. In this case, the strong correlation between "amount of bill" and "number of diners" (as indicated in the correlation matrix) suggests multicollinearity.

c. The multiple regression equation provides a model for predicting tips based on both "amount of bill" and "number of diners." The coefficients (-6.7571, 0.1504, 2.5123) represent the intercept and slopes, respectively.

d-2. The coefficient of determination ((R²)) explains the proportion of the variance in the dependent variable ("amount of tip") that can be predicted from the independent variables. In this case, (R² = 0.8536) indicates a high explanatory power of the model.

e. Using the regression equation, the predicted tip for a $100 bill is calculated to be approximately $12.193.

f. The statement that "residuals look random" indicates that the errors between predicted and observed values are not systematically related. This is a desirable characteristic in regression analysis, suggesting that the model is appropriate for the data.