Question

The advertising revenue (in billions of dollars) of Company A is given for various quarters of 2015 and 2016. Let x = 1 correspond to the first quarter of 2015.

Advertising Revenue of Company A

Quarter	Revenue
1	10.2
2	11.3
3	13.1
4	16.2
5	14.6
6	14.1
7	15.3
8	15.7

(a) If the advertising revenue was 10.2 billion dollars in the first quarter of 2015 and 16.2 billion dollars in the fourth quarter of 2015 find a linear model for the quarterly revenue and use this model to estimate the advertising revenue in the first quarter of 2017 assuming the trend continues.

(b) Use the data given to find the least-squares regression line and find the correlation coefficient. (Approximate values to three decimal places.) (c) If this trend continues, what will the revenue be in the first quarter of 2017?

(d) Compute the sum of the squares of the residuals for each of the linear models from part (a) and part (b).

Answer 1

(revenue Y in &on! (0) 16-21 10.2 cX,Y) in the 625 YOYO Xe corresponds to quarter) por a linear model y = mx tb m = Yey = 16.2-10.2 X- x u . 1 putting b= y, -mx, = 10:2-20L = 82 (X,Y) equation Therefore, linear Therefore, linear model model is Y=2x+812 for first quarter of 2017 x=9: ... Revenue = 2 x 9 +0.2 = 26.2 bn dollor 6 x y z ă Y Ý (8-5) 2 GX *(4- y.g² I 10.2 -3.6 -3.6 12.25 12.60 12.96 6:25 11.3 -1.5 13.1 -0.7 2.25 25 -1-20 4 16.2 2.4 -0.5 25 +0.5 0-40 14.6 018 4.60 2.25 +1.5 14.1 0.3 -09 6:25 3.75 2.25 7 15-3 12.25 3.61 42.00 34.00 x=265 Ý= 13-8 for least squares repression line y-m%cto we can find m= (x-x) *ly 7) = 34.00 – 0.81 42.00 {(x-x)2 parting (1, 10:2) in the egn: 6:10.2-0.81 L = 9.39 So least squares repression Une is : y = 0.81%+939 (x-x)*(y-7) Pearson's correlation coefficient (1) - =) re 12+ 32.05 = 36.689 = 0.927 +2.5 +3.5 1.9 665 8 15.7 37:05 34 Ext) 2 * {xyz =) re 34

for the first quarter of pon Revenue (y): 0.0*9 + 9.39 = x=9 16.60 bn dollar O (d) Residuals from model in part @ actual y estimated y resiаual residual) 2 10.2. 10.2 0.9 122 0.81 11.3 1.21 13.1 142 0.0 16.2 162 0 5.76 146 102 3.6 6.6 37.21 15.3 6.9 47.61 15-7 72.25 estimated y=2x; + 8.2 164.05 residual = (estimated y actual y . Sum of residual squares = 164.85 در یک مولده 22.2 २५२ 10g Residuals from model in part 6 X Lactual) Y cestimated) residual esidual) 2 10.2 11.3 11.04 -0.29 0.004 131 11.02 1:20 1-630 16.2 12.63 -3.57 +2.75 12.745 14.6 13.44 -116 1. 345 14.1 14.25 0.15 0.023 15.3 15.06 -0.24 15-7 0.17 0.029 y costimated) = 0.PL X ; +9.89 15.02 residual = ( Yestimated - Yocual) in sum of residual squares = 15.92 0-057 15.07