A waiter at a restaurant wanted to predict her next tip base

A waiter at a restaurant wanted to predict her next tip based on the bill the customers would receive.

Receipts: Bill & Tip

Bill Tip

25.4 3.5

32.6 4.2

15.2 4.3

22.2 5.3

31.1 16.8

16.0 8.6

22.1 12.6

A) Which of the following statements is true?

B) Using the results provided here, calculate the slope of the least squares regression line for the data.

Bill Tip

Mean 23.51 7.9

Standard Deviation 6.74 5.08

Correlation Coefficient .229 .229

C) Using the results previously obtained, calculate the intercept of the least squares regression line for the data.

D) Using the results previously obtained, state the regression equation used to predict tip using bill:

E) Use the regression equation to predict the Tip for a Bill = 23.45.

the waitor wanted to predict her next tip based on the bill the customers would receive.

so here bill is the predictor and tip is the response variable.

let tip=Y and bill=X

so we need to predict Y on the basis of X

let the least square regression equation be Y=a+bX

where a is the intercept and b is the slope.

B) we know b=r*s_y/s_x where r is the correlation coefficient s_y is the standard deviation of tip and s_x is the standard deviation of bill.

now r=0.229 s_y=5.08 s_x=6.74

so slope=0.229*5.08/6.74=0.1726

C)we know that intercept =a=mean of tip-b*mean of bill=7.9-0.1726*23.51=3.842174

D) hence the regression equation is tip=3.842174+0.1726*bill [putting the values of a and b in Y=a+bX]

E) now when bill=23.45 then predicted value of tip is [by putting bill=23.45 in the regression equation]

tip=3.842174+0.1726*23.45=7.889644 [answer]