Question

3.5          Drop/remove the insignificant independent variable from the regression model, and develop and show an updated estimated regression equation that can be used to predict the average annual salary for salaried employees given the average annual salary for hourly employees and the size of the company. Again, use the F test and α = 0.05 to test for overall significance. Also use the t test and α = 0.05 to determine the significance of the independent variables in this updated estimated regression equation How much percentage of the variability in y is explained by the updated estimated regression equation? (15 points)

Rank	Company	Size	Salaried ($1000s)	Hourly ($1000s)	Midsize	SmallSize
4	Wegmans Food Markets	Large	56	29	0	0
6	NetApp	Midsize	143	76	1	0
7	Camden Property Trust	Small	71	37	0	1
8	Recreational Equipment (REI)	Large	103	28	0	0
10	Quicken Loans	Midsize	78	54	1	0
11	Zappos.com	Midsize	48	25	1	0
12	Mercedes-Benz USA	Small	118	50	0	1
20	USAA	Large	96	47	0	0
22	The Container Store	Midsize	71	45	1	0
25	Ultimate Software	Small	166	56	0	1
37	Plante Moran	Small	73	45	0	1
42	Baptist Health South Florida	Large	126	80	0	0
50	World Wide Technology	Small	129	31	0	1
53	Methodist Hospital	Large	100	83	0	0
58	Perkins Coie	Small	189	63	0	1
60	American Express	Large	114	35	0	0
64	TDIndustries	Small	93	47	0	1
66	QuikTrip	Large	69	44	0	0
72	EOG Resources	Small	189	81	0	1
75	FactSet Research Systems	Small	103	51	0	1
80	Stryker	Large	71	43	0	0
81	SRC	Small	84	33	0	1
84	Booz Allen Hamilton	Large	105	77	0	0
91	CarMax	Large	57	34	0	0
93	GoDaddy.com	Midsize	105	71	1	0
94	KPMG	Large	79	59	0	0
95	Navy Federal Credit Union	Midsize	77	39	1	0
97	Schweitzer Engineering Labs	Small	99	28	0	1
99	Darden Restaurants	Large	57	24	0	0
100	Intercontinental Hotels Group	Large	63	26	0	0

Answer 1

From the data it is seen that "Midsize" and "SmallSize" are two dummy variables created from the "Size" variable. Now while fitting regression model, it automatically creates dummy variables for categorical variables, so I am dropping the "Midsize" and "SmallSize" variables to avoid multicollinearity.

So finally fitting the linear regression model where response is "Salaried" and explanatory variables are "Hourly" and "Size". Below is the result of the model summary.

So from the result, it is seen that the F-statistic value is 11.72 and corresponding p-value is 4.817e-05 which is very very less than 0.05. This strongly tells that the model is overall significant.

Moreover, the p-value of the explanatory variables are less than 0.05 informing that both the Hourly and Size variable are significant in predicting Salaried variable.

R² = 0.5749. Then 57.49% of variability of y is explained by the updated regression Model.