Question

A study was made by a publishing company on how advertising costs for the company correlated with sales.

1. Find the equation of the regression line to predict sales from advertising costs.
2. Estimate the weekly sales when advertising costs are 35TL.

Advertising costs	Sales
50	530
35	410
45	360
90	790
60	710
60	480

Answer 1

х Y X*Y x2 y2 50 530 26500 2500 280900 35 410 14350 1225 168100 45 360 16200 2025 129600 90 790 71100 8100 624100 60 710 42600 3600 504100 60 480 28800 3600 230400 Sum = 340 3280 199550 21050 193720 0
from above table we calculate
340 X = X; = 56.666 6 η 3280 Y Σ = 546.666 n 6 i=1 2 SSxx = ΣΧ? Σx: (Σ = 21050 - 340? /6 = 1783.333 i=1 2 (Σχ.) 1850, - Σκι - Σ) 15αν - Σκη (Σκ) (Ση). 1937200 - 3280? /6 = 144133.333 = 199550 - 340 x 3280/6 = 13683.333

Let m be the slope and n be the y intercept

according to question when X is 35

SSXY m = 13683.333 1783.333 = 7.6729 SSxx n= Ï - Ì. . m = 546.666 - 56.666x7.6729 = 111.8692 regression equation is: Y = 111.8692 + 7.6729X

So according to regression equation sales for 35TL is

Y=111.8692+7.6729×35= 380.4207