Question

The amounts of 6 restaurant bills and the corresponding amounts of the tips are given in the below. Assume that bill amount is the explanatory variable and tip amount the response variable. BillTip43.585.5088.0110.00106.2716.0052.447.0049.725.2870.2910.00 Bill 43.58 88.01 106.27 52.44 49.72 70.29 Tip 5.50 10.00 16.00 7.00 5.28 10.00

(a) Find the correlation: ?= r = ____ (b) Does there appear to be a significant correlation? A. No B. Yes (c) The regression equation is ?̂= ____ (d) If the amount of the bill is $95, 95 , the best prediction for the amount of the tip is $ equation editorEquation Editor . Note: Enter your answer as a number xx.xx (e) According to the regression equation, for every $5 increase in the bill, the tip should (Enter INCREASE or DECREASE) by $______

Answer 1

a. First we will find r

X Values
∑ = 410.31
Mean = 68.385
∑(X - M_x)² = SS_x = 3041.956

Y Values
∑ = 53.78
Mean = 8.963
∑(Y - M_y)² = SS_y = 81.08

X and Y Combined
N = 6
∑(X - M_x)(Y - M_y) = 474.866

R Calculation
r = ∑((X - M_y)(Y - M_x)) / √((SS_x)(SS_y))

r = 474.866 / √((3041.956)(81.08)) = 0.9562

b. As r is near to 1, it is significant

c.

Sum of X = 410.31
Sum of Y = 53.78
Mean X = 68.385
Mean Y = 8.9633
Sum of squares (SS_X) = 3041.9562
Sum of products (SP) = 474.8663

Regression Equation = ŷ = bX + a

b = SP/SS_X = 474.87/3041.96 = 0.1561

a = M_Y - bM_X = 8.96 - (0.16*68.39) = -1.7120

ŷ = 0.1561X - 1.7120

d. Now for x=95, y=0.1561*95-1.7120=13.12