Simple Regression - Simple Regression a F=MSR/MSE...

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Simple Regression a. F=MSR/MSE = (60/1)/(40/18) = 27 b. Fcrit = 4.41 c. Fcalc> Fcrit, therefore reject null hypothesis that there is no significant relationship between X and Y. d. r 2 = SSR/SST = 60/100 = 0.6, r = -0.775 There is evidence of a relationship between shelf space and sales at the 0.05 level (Fcalc (21.639) > Fcrit (4.84). Also note the t-stat for space – indicates it is significant at the 0.05 level. There is evidence of a relationship between shelf space and sales at the 0.05 level (Fcalc (21.639) > Fcrit (4.84). Also note the t-stat for space – indicates it is significant at the 0.05 level. 95% CI for 1: CI: 0.074 2.2281(0.0159) 0.074 0.035 0.039< 1< 0.109 d. R 2 ~ 0.683 indicates a moderately strong predictive relationship. The value indicates that around 68.3% of the variation in sales can be explained by the variation in shelf space available. The standard error of the estimate indicates that around 68% of the actual Y values (sales) will fall within ~ $0.31 of the regression line. c. Hypothesis test needed H0: =0 H1: 0 =0.05 n=7 Test statistic: 1 1 b b t s = (11.20 – 0)/ 4.8344) = 2.317 (rounded values)
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  • Spring '14
  • Garofalo,LB
  • Statistics, Null hypothesis, Statistical hypothesis testing, Type I and type II errors, Statistical power, work shift

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