Question

During a research, the amount of Internet users was measured. Each time three random groups of 10,000 people of the average age of 20, 40, and 60 were considered. The data are as follows (x1 - the number of years since the beginning of the research, x2 - age, y - number of users):

Reserve Problems Chapter 12 Section 1 Problem 1 During a research, the amount of Internet users was measured. Each time three random groups of 10,000 people of the average age of 20, 40, and 60 were considered. The data are as follows (x1 - the number of years since the beginning of the research, X2 - age, y - number of users): X1 1700 1450 220 3300 2800 570 4750 44101110 6490 5930 1520 1 1 1 3 3 3 5 5 5 7 7 7 20 40 60 20 40 60 20 40 60 20 40 60 22 (a) Fit a multiple linear regression model using Xi and X2 as the regressors. Round your answers to one decimal place (e.g. 98.7) 9= x+ (b) Estimate o? Round your answer to the nearest Integer (e.g. 9876). (c) Find the standard errors of the regression coefficients. Round your answers to one decimal place (e.g. 98.7) selo) se(B.) = se(B2) = (d) Use the model to predict the number of users in random group of 40 years after 4 years of research Round your answer to the nearest integer (e.9. 9876). Number of users nes)

Answer 1

## R command

y=c(1700,1450,220,3300,2800,570,4750,4410,1110,6490,5930,1520)
x1=c(1,1,1,3,3,3,5,5,5,7,7,7)
x2=c(20,40,60,20,40,60,20,40,60,20,40,60)

model=lm(y~x1+x2)
summary(model)

## End

> y=C(1700, 1450, 220, 3300, 2800,570, 4750, 4410, 1110, 6490,5930, 1520) > x1=C(1,1,1,3,3,3,5,5,5,7,7,7) > x2=C (20,40, 60,20, 40, 60,20, 40, 60, 20, 40, 60) > model=1m (yºx1+x2) > summary (model) Call: Im (formula = y - x1 + x2) Residuals: Min 10 -1497.17 -608.67 Median 87.33 30 584.21 Max 1310.33 1 Coefficients: Estimate Std. Error t value Pr(tl) (Intercept) 3705.17 861.30 4.302 0.001985 ** x1 588.50 120.61 4.880 0.000872 *** x2 -80.13 16.51 -4.852 0.000906 *** Signif. codes: 0.001 *** 0.01 * 0.05.' 0.11 Residual standard error: 934.2 on 9 degrees of freedom Multiple R-squared: 0.8403, Adjusted R-squared: 0.8048 F-statistic: 23.67 on 2 and 9 DE, p-value: 0.0002601

a ) The regression equation is ŷ =3705,17 +588,50 - 80.13 xa. +(934.2) = 872729,6 c) = 861.3 = 120.6 seeße) = 16.5 The number of users in rondom group of 40 years after 4 years of research is =3705.17t588.50% 4-8.0.134 40 - 2853.97 Number of users = 2854.