Question

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): y 1600 1350 200 3200 2700 550 4650 4310 | 1010 6390 5830 1420 X] 1 1 1 3 3 3 5 5 5 7 7 7 20 60 20 40 60 60 20 40 60 40 20 40 (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). + bri+ X2 (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). se se(Bo) = 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.g. 9876). Number of users =

Answer 1

Sol:

Install analysis toolpak in excel

Data >Data analysis>Regression

un 60 1010 6390 7 20 Input Y Range: a1:a13 5830 7 40 Input X Range: b1:13 1420 7 60 Labels O Constant is Zero Confidence Level: 95 % Output Range: D$2 O Residuals O Residual Plots Standardized Residuals Vindows Line Fit Plots to PC settings to activate Window n Normal Probability Plots 0 Sheet4 Sheet7 anova Sheets Sheet2

we get

ANOVA df SS Regression Residual Total 2 9 MS F Significance F 40439451.67 20219726 22.85296 0.000297 7962973.333 884774.8 48402425 11 Intercept x1 Coefficients Standard Error t Stat P-value Lower 959 Upper 95 3599.833333 867.2131183 4.151037 0.002481 1638.061 5561.606 583.1666667 121.4341258 4.802329 0.000971 308.4636 857.8697 -79.125 16.62805249 -4.75852 0.001032 -116.74 -41.5097

ANSWER(A)

y^=3599.8+583.2*x1+-79.1*x2

ANSWER(B)

common variance=MS residual=884775

ANSWER(C)

se(beta0)=867.2

se(beta1)=121.4

se(beta2)=16.6

ANSWER(D)

y^=3599.8+583.2*4-79.1*40

y^=2768.6

y^=2769