2). These data relate y (a measure of surface finish), to x (lathe speed in RPM)

Question

2). These data relate y (a measure of surface finish), to x (lathe speed in RPM). 10 measurements are taken on one type of lathe (A), and 10 measurements on another (B). Thus we have n-20 measurements, and "Lathe Type" is an indicator (dummy) variable which has two levels A: x225 200 250 245 235 237 265 259 221 218 B: x 224 212 248260 243 238224251 232 216 45.44 42.0350.1 48.7547.92477952.2650.5245.5844.78 y 33.5 31.23 3752 37.13 34.7 33.92 32.13 35.47 3349 32.29 a). Find: the least squares line: y = R2 R2 adj = b). Use a dummy variable, and fit the model that allows for different intercepts for the two lathe types but the same slope. Give the estimates for the following, and R2 for this model. variable, and fit the model that allows for different intercepts for the two lathe types but Lathe A intercept . Lathe B intercept , slope . adj

Explanation / Answer

From Excel

a)

The Regression equation is

y=5.777 + 0.149 (x)

where slope=0.149 and intercept=5.777

R2 =0.128

R2 adjusted =0.079

SUMMARY OUTPUT Regression Statistics Multiple R 0.357864 R Square 0.128067 Adjusted R Square 0.079626 Standard Error 7.02869 Observations 20 ANOVA df SS MS F Regression 1 130.6091 130.6091 2.643776 Residual 18 889.2447 49.40248 Total 19 1019.854 Coefficients Standard Error t Stat P-value Intercept 5.776808 21.61402 0.267271 0.792298 X 0.149057 0.091673 1.625969 0.121336

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