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. Bill 88.01 43.58 Tip 10.00 5.50 64.30 7.70 32.98 4.50 106.27 16.00 49.72 5.28 (a) Find the correlation: r= (Keep at least 3 digits after the decimal point.) (b) Does there appear to be a significant correlation? A. Yes B. No . (write in the form b0+b1*x, and keep at least 3 digits after the decimal (c) The regression equation is ĝ = point.) . (Enter your answer in dollars: $ (d) If the amount of the bill is $80, the best prediction for the amount of the tip is XX.xx) (Enter (e) According to the regression equation, for every $5 increase in the bill, the tip should INCREASE or DECREASE in capital letter) by (f) Calculate the proportion of the variability explained by the regression line. (Enter your answer as a percent): %

Answer 1

a.

X-M X-M CY-My) Y-My (X-MJY-My) 569.618 23.867 1.837 43.835 3.373 7.893 -20.563 -2.663 54.767 422.851 e.025 -0.073 e.157 -0.463 0.215 -31.163 -3.663 114.162 971.153 13.420 42.127 7.837 1774.656 330.133 61.413 -2.883 -14.423 41.587 208.033 8.314 Sum 584.411 MX: 64.143 Мy: 8.163 Sum 3946.335 Sum: 93.828

X Values
∑ = 384.86
Mean = 64.143
∑(X - M_x)² = SS_x = 3946.335

Y Values
∑ = 48.98
Mean = 8.163
∑(Y - M_y)² = SS_y = 93.828

X and Y Combined
N = 6
∑(X - M_x)(Y - M_y) = 584.411

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

r = 584.411 / √((3946.335)(93.828)) = 0.960

b.

X Values Y Values

From figure we are confirm that r is significant

c.

х-м,? (X- MJ(Y- M,) X-M Y-My 23.8667 1.8367 43.8351 569.6178 54.767 422.8507 .0245 971.1533 1774.656 288.0325 -20.5633 -2.6633 0.1567 -0.4633 -0.0726 3.6633 31.1633 114.1617 7.8367 42.1267 330.1326 41.5873 -14.4233 -2.8833 SP: 584.4111 SS: 3946.3349

Sum of X = 384.86
Sum of Y = 48.98
Mean X = 64.1433
Mean Y = 8.1633
Sum of squares (SS_X) = 3946.3349
Sum of products (SP) = 584.4111

Regression Equation = ŷ = b1X + b0

b1 = SP/SS_X = 584.41/3946.33 = 0.148

b0= M_Y - b1M_X = 8.16 - (0.15*64.14) = -1.336

ŷ = 0.148X - 1.336

d. For x=80,

ŷ = (0.148*80) - 1.336=10.504