Question

E ៥ដង А B c D 1 DATA SET FOR SALESFORCE PROBLEM 2 3 4 D No, SALES TEST MONTHS 5 86 6 2 105 62 48 7 3 8 4 9 5 10 106 68 63 11 100 12 8 115 13 9 78 14 10 101 64 15 11 115 117 16 12 120 103 17 13 88 49 18 14 110 87 110 15 77 16 60 17 18 19 115 20 95 84 102 24 100 71 68 61 75 71 28 106 113 114 110 98 92 106 76 83 81 31 32 79 85 102 102 88 105 38 66 94 +86 42 99 61 75 71 82 46 115 114 110 98 92 106 103 111 76 83 81 79

1. Using simple regression, determine whether test scores are significantly related to sales performance. Use significance level of 0.05%. Clearly interpret the slope (beta coefficient) and the adjusted R squared value you obtained.
2. Using multiple regression, determine whether test scores and number of months are significantly related to sales performance. Use significance level of 0.05%. Clearly interpret the slopes (beta coefficients) and the adjusted R squared value you obtained.

Answer 1

a.

R output:

Call: im (formula = Sales Test) Residuals: Min 10 -23.6223 -6.9053 Median -0.6825 30 6.1428 Max 16.1369 Coefficients: Estimate Std. Error t value Pr(+1) (Intercept) 83.0686 10.0236 8.287 6.97e-11 *** Test 0.2651 0.1357 1.954 0.0565 Signif. codes: 0 ***' 0.001 ***' 0.01 '*' 0.05 .' 0.1'' 1 Residual standard error: 9.126 on 49 degrees of freedom Multiple R-squared: 0.07226, Adjusted R-squared: 0.05332 F-statistic: 3.816 on 1 and 49 DF, p-value: 0.05648

Since p-value corresponding F statistic=0.05648>0.05, there is insufficient evidence to conclude that test scores are not significantly related to sales performance at significance level of 0.05.

As Test score is increased by one unit expected Price is increased by 0.2651 unit. The value of adjusted R-squared=0.05332 is very small hence fitting is not good.

R code:

Sales=c(122,105,103,95,97,106,100,115,78,101,115,120,88,110,96,93,
92,103,121,95,99,102,98,100,99,99,113,114,110,98,92,106,103,111,102,102,88,105,
94,108,84,99,99,113,114,110,98,92,106,103,111)
Test=c(86,62,85,72,78,68,79,67,70,64,84,84,56,87,82,65,70,64,83,84,69,82,81,68,61,
75,71,79,76,83,81,79,84,55,54,74,65,66,62,79,59,61,75,71,79,76,83,81,79,84,55)
m=lm(Sales~Test)
summary(m)

b. R output:

Call: Im (formula = Sales - Test + Month) Residuals: Min 19 -20.144 -4.679 Median -1.011 30 7.478 Max 19.752 Coefficients: Estimate Std. Error t value Pr(>It) (Intercept) 86.01524 9.23219 9.317 2.44e-12 *** Test -0.03020 0.15459 -0.195 0.84595 Month 0.24141 0.07509 3.215 0.00234 ** Signif. codes : 0 ****' 0.001 *** 0.01 ** 0.05.' 0.1 1 Residual standard error: 8.364 on 48 degrees of freedom Multiple R-squared: 0.2366, Adjusted R-squared: 0.2048 F-statistic: 7.439 on 2 and 48 DF, p-value: 0.001533

Since p-value corresponding F statistic=0.001533<0.05, there is sufficient evidence to conclude that the regression equation is significant. However "Test" is insignificant (since its p-value=0.84595>0.05) and "Month" is significant (since its p-value=0.00234<0.05). Hence  number of months are significantly related to sales performance.

As Test score is increased by one unit and number of months is kept fixed then the expected Price is decreased by 0.03020 unit. As number of months is increased by one and Test score is kept fixed then the expected Price is increased by 0.24141 unit.The value of adjusted R-squared=0.2048 is very small hence fitting is not good but this value is significantly larger than previous model in (a) hence this is improved model than Part (a).