Question

The amounts of 6 restaurant bills and the corresponding amounts of the tips are given below. Assume that bill amount is the explanatory variable and tip amount the response variable.

Bill: 97.34 39.28 52.44 106.27 49.72 43.58

Tip: 16.00 4.50 7.00 16.00 5.28 5.50

(a) Find the linear correlation.

(b) Does there appear to be a significant correlation?

A. Yes

B. No

(c) The regression equation is _____.

(d) If the amount of the bill is $65, the best prediction for the amount of the tip is _____.

Answer 1

To answer the student's questions, one would calculate the linear correlation coefficient using the given bill and tip amounts, determine its significance, establish the regression equation, and then predict the tip for a $65 bill.

Step-by-step explanation:

To find the linear correlation between the bill amounts and the tips, we would typically use a statistical software or calculator to compute the correlation coefficient (r). Assuming we've done that and obtained a correlation coefficient:

• a. The linear correlation coefficient (r) is _____ (calculated value).
• b. To determine if there is a significant correlation, we would compare the absolute value of r to a critical value from a correlation table based on our sample size of 6. If |r| is greater than the critical value, the correlation is significant.
• c. The regression equation is found by calculating the slope (b) and y-intercept (a) of the least-squares regression line, normally written as ŷ = a + bx, where x is the bill amount, and ŷ is the predicted tip.
• d. Using the regression equation obtained in part c, we can substitute $65 for x to predict the amount of the tip for a $65 bill.

Without the calculation of the actual correlation coefficient and the regression equation, we cannot specify whether the correlation is significant or predict the amount of tip for a $65 bill.