Question

Part 1: Model Building

1. Submit both this word and excel file

2. Keep two decimal places for your answer

Using the data Reynolds.xls. The variables are defined as:

Sales (Y) =number of electronic laboratory scales sold

Months (X) =the number of months the salesperson has been employed

1. Develop the scatter plot using Sales as y axis and Months as x axis, and can you see the curvature?

2. Using a simple linear regression model to develop an estimated regression equation to predict the Sales. What is the adjusted-R square?

3. Using a second-order regression model to develop an estimated regression equation to predict the Sales. What is the adjusted-R square? (Hint: second-order regression model should look like: y=b0+b1X+b2X2, and we learnt it in Chapter 16)

4. Compare the adjusted-R square from 2 and 3, which one is larger? Which model is better? (Hint: we learn this in Chapter 15)

5. Use 4 diagrams to test the 5 model assumptions for the second-order regression model. Do you think they are violated? (Hint: we learn this in week 12 computer skill class)

Months	Sales
41	275
106	296
76	317
104	376
22	162
12	150
85	367
111	308
40	189
51	235
9	83
12	112
6	67
56	325
19	189

Answer 1

scatter plot ## 1) scatter plot sales as y axis and months as x axis 350 yes from plot it see curveture because data points are scatter such way 250 150 100 50 ### 2) simple regression model estimated value for y is vhat b0+b1x 100 20 40 60 Months b0 intercept b1 slope adjusted R square value is 0.764341 111.2279 2.376775 SUMMARY OUTPUT Regression Statistics Multiple 0.88384 R Square 0.781174 Adjusted I 0.764341 Standard 49.5158 Observati ANOVA MS gnificance F Regressio Residual Total 1 113783.3 113783.3 46.40781 1.24E-05 13 31873.59 2451.815 14 145656.9 15 P-value Intercept 111.2279 21.628 5.142774 0.000189 64.50346 157.9524 64.50346 157.9524 Months(x 2.376775 0.348893 6.812328 1.24E-05 1.623037 3.130513 1.623037 3.130513 Coefficientandard Err Lower 95%Up er 95%ower 95.0 p er 95.0% t Stat

SUMMARY OUTPUT 4) second order model is yhat-b0+b1*x+b2*x2 Regression Statistics Multiple F 0.949847 R Square 0.902209 Adjusted I 0.885911 Standard 34.45277 Observati ANOVA MS gnificance F b0 b1 b2 45.34758 6.344807 0.03449 Regressio Residual Total 2 131413 65706.5155.35542 8.75E-07 12 14243.92 1186.993 14 145656.9 15 Adjusted R square vale is 0.885911 from 2 and 3 adjusted R square is larger for 3 hence 3 second order model is good than simple regression model P-value Intercept 45.34758 22.774651.991142 0.069734.27413 94.969294.27413 94.96929 Months(x 6.344807 1.057851 5.997824 6.24E-05 4.039947 8.649667 4.039947 8.649667 coefficientandard Err Lower 95%Upper 95%ower 95.09 pper 95.0% t Stat 0.03449 0.008948 -3.85388 0.002294 -0.05398-0.01499 -0.05398-0.01499 adjusted R squre or R square is large then model is very good 4 diagrams are scatter plot, Residual plot for x1 and x2, Normal probability plot, x1 and x2 fit plot

4 diagrams are scatter plot, Residual plot for x1 and x2, Normal probability plot, x1 and x2 fit plot here residual plot for x2 is violated because some points are not scattered well RESIDUAL OUTPUT PROBABILITY OUTPUT Percentile Sales(y) fit plot for x1 and x2 is curvature in trend that is not in linear Observatiordicted Sale. Residuals dard Residuals 1 247.5144 27.48563 0.861698 2 330.4169-34.4169 1.079 3 328.3641 -11.3641 0.35627 4 332.2113 43.78874 1.372814 5 168.2423-6.24230.1957 6 116.5193 33.480661.049647 7 335.4977 31.50228 0.987623 8 324.7241 -16.72410.52431 9 243.9629 -54.9629 1.72313 10 279.2357-44.2357-1.38683 11 99.65751 -16.6575-0.52223 12 116.5193-4.51934-0.14169 13 82.17494 -15.1749-0.47575 14 292.5099 32.49007 1.018591 15 153.4496 35.55039 1.114535 3.333333 10 16.66667 23.33333 30 36.66667 43.33333 50 56.66667 63.33333 70 76.66667 83.33333 90 96.66667 83 112 150 162 189 189 235 275 296 308 317 325 367 376 here Normal probability plot for x vs y is linear hence it is good and assumption satisfied Normal Probability Plot 300 -200 100 0 20 40 60 80 100 120 Sample Percentile

Months(x) Line Fit Plot x2 Line Fit Plot 400 s300 -200 400 300 200 100 0 ◆ Sales(v) Sales(y) Predicted Sales(y) Predicted Sales(y) 0 100 0 50 150 5000 10000 15000 Months(x) x2 Months(x) Residual Plot x2 Residual Plot 50 50 60 40 80 100 120 15000 5000 10000 -50 -50 100 -100 Months(x) x2