Question

1. The following data set (columns C1 thru C4 of exam2.mtw) attempts to model the annual salary (in thousands of dollars) of a random sample of n=20 high school mathematics teachers using years of teaching experience and geographic location (0= South, and 1=North). The data set is given below. The same data set and Minitab output is provided exam2.mtw.

            Your model should first be built in order to answer all of the following research    questions. Make certain you have acceptable diagnostics and/or you have made an acceptable transformation. Can you help me with transforming the data? I think I need to transform X after looking at residuals, but im not sure or how to. If this could be done in Minitab that would be best or just an explanation please

Question Data

Salary	Experience	Location	Exp*Loc
30.95	10	0	0
29.22771	8	0	0
24.63187	6	0	0
23.97167	4	0	0
24.07303	6	0	0
29.8492	10	0	0
29.58699	11	0	0
20.36082	3	0	0
66.56994	15	1	15
73.03498	16	1	16
65.5	12	1	12
39.65	3	1	3
43.43299	5	1	5
30.6017	2	1	2
24.0629	1	1	1
36.44486	3	1	3
41.75	6	1	6
49.86652	9	1	9
46.55308	8	1	8
41.0261	7	1	7

Answer 1

Sol:

Console-> sal=c(30.95,29.2277,24.6319,23.9717,24.073,29.8492, 29.5870,20.3608,66.56 99,73.035,65.5,39.65,43.433,30.6017,24.0629,36.4449,41.75,49.8665,46.5531, 41.0261) > sal [1] 30.9500 29.2277 24.6319 [4] 23.9717 24.0730 29.8492 [7] 29.5870 20.3608 66.5699 [10] 73.0350 65.5000 39.6500 [13] 43.4330 30.6017 24.0629 [16] 36.4449 41.7500 49.8665 [19] 46.5531 41.0261 > exp=C(10,8,6,4,6,10,11,3,15,16,12,3,5,2,1,3,6,9,8,7) > exp [1] 10 8 6 4 6 10 11 3 15 [10] 16 12 3 5 2 1 3 6 9 [19] 8 7 > loc=c(0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1) > loc [1] 00000000111111 [15] 111111 > exploc=exp* loc > exploc [1] 0 0 0 0 0 0 0 0 15 [10] 16 12 3 5 2 1 3 6 9 [19] 8 7 > #all the data is now prepared now let's do the regression analysis > regression=lm(sal-exp+loc+exploc) > summary(regression)

> summary(regression) call: Im(formula = sal exp + loc + exploc) Residuals: Min 1Q Median -4.7862 -1.6082 -0.5325 Max 5.4984 30 1.4389 Coefficients: Estimate std. Error (Intercept) 17.7697 2.9515 exp 1.2154 0. 3802 loc 7.6364 3. 3420 exploc 1.6998 0.4210 t value pr(t) (Intercept) 6.021 1.78e-05 exp 3.196 0.005620 loc 2.285 0.036302 exploc 4.037 0.000954 (Intercept) exp loc exploc signif. codes: 0.***' 0.001 '**' 0.01 %! 0.05 '.' 0.1''1 Residual standard error: 2.982 on 16 degrees of freedom Multiple R-squared: 0.9681, Adjusted R-squared: 0.9621 F-statistic: 161. 8 on 3 and 16 DF, p-value: 3.534e-12 > #a) since p value of location is 0.036302 which is significantly less (f or 95% conf less than 0.05) we can say that yes , location is significant in finding the salary > #b) the p value of years of exp is 0.00562 which is very very less than 0.05 experiencce is highly significant for predicting salary > cor (exp, loc) [1] o > cor(loc, exp) [1] 0 > #c) since the correlation coefficient of experience and location and vic e versa has is o we can conclude that there is no influance of exp on loc and vice versa > cor (sal[1:8], exp[1:8]) #for loc=0 [1] 0.9465456 > cor (sal[9:20], exp[9:20]) #for loc=0 [1] 0.9726945 > #d&e) since the correlation coefficient of salary and exp for south as w ell as north are 0.9466 and 0.9727 we conclude that there is high influenc e that years of experience has on salary for both south as well as north >