Consider the following sample data y 46 51 28 55 29 53 4736 X1 40 48 29 44 30 58

Question

Consider the following sample data y 46 51 28 55 29 53 4736 X1 40 48 29 44 30 58 60 29 X2 13 28 24 11 28 28 29 14 &Click; here for the Excel Data File a-1. Estimate a multiple linear regression model. (Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.) y-hat- X1 + X2 a-2. Interpret its coefficients X1 O As x1 increases by one unit, y is predicted to increase by 22.81 units, holding x2 constant. O As x increases by one unit, y is predicted to decrease by 0.85 units, holding x2 constant. O As X1 increases by one unit, y is predicted to increase by 0.85 units, holding X2 constant O As x1 increases by one unit, y is predicted to decrease by 22.81 units, holding x2 constant. a-3. Interpret its coefficients X2. O As x2 increases by one unit, y is predicted to decrease by 22.81 units, holding x1 constant. As X2 increases by one unit, y is predicted to increase by 0.71 units, holding X1 constant. As X2 increases by one unit, y is predicted to decrease by 0.71 units, holding x1 constant. O As x2 increases by one unit, y is predicted to increase by 22.81 units, holding xi constant. b. Find the predicted value for y if x1 equals 50 and x2 equals 20. (Round the intermediate coefficient values to 2 decimal places. Round your answer to 2 decimal places.) y-hat

Explanation / Answer

applying regression:

a-1)

yhat =22.81+0.85x1+(-0.71) x2

a-2) as x1 increase by one unit ; y is predicted to increase by 0.85 units ; holding x2 constnat

a-3)

as x2 increase by one unit ; y is predicted to decrease by 0.71 units ; holding x1 constant

b) yhat =22.81+0.85*50-0.71*20=51.11

Regression Statistics Multiple R 0.9291 R Square 0.8632 Adjusted R Square 0.8085 Standard Error 4.6868 Observations 8 ANOVA df SS MS F Significance F Regression 2 693.05 346.52 15.78 0.0069 Residual 5 109.83 21.97 Total 7 802.88 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 22.8074 6.8384 3.3352 0.0207 5.2288 40.3861 x1 0.8460 0.1523 5.5546 0.0026 0.4545 1.23757 x2 -0.7053 0.2451 -2.8773 0.0347 -1.3353 -0.07517

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