Question

 

SALARY	EDUC	EXPER	TIME
39000	12	0	1
40200	10	44	7
42900	12	5	30
43800	8	6	7
43800	8	8	6
43800	12	0	7
43800	12	0	10
43800	12	5	6
44400	15	75	2
45000	8	52	3
45000	12	8	19
46200	12	52	3
48000	8	70	20
48000	12	6	23
48000	12	11	12
48000	12	11	17
48000	12	63	22
48000	12	144	24
48000	12	163	12
48000	12	228	26
48000	12	381	1
48000	16	214	15
49800	8	318	25
51000	8	96	33
51000	12	36	15
51000	12	59	14
51000	15	115	1
51000	15	165	4
51000	16	123	12
51600	12	18	12
52200	8	102	29
52200	12	127	29
52800	8	90	11
52800	8	190	1
52800	12	107	11
54000	8	173	34
54000	8	228	33
54000	12	26	11
54000	12	36	33
54000	12	38	22
54000	12	82	29
54000	12	169	27
54000	12	244	1
54000	15	24	13
54000	15	49	27
54000	15	51	21
54000	15	122	33
55200	12	97	17
55200	12	196	32
55800	12	133	30
56400	12	55	9
57000	12	90	23
57000	12	117	25
57000	15	51	17
57000	15	61	11
57000	15	241	34
60000	12	121	30
60000	15	79	13
61200	12	209	21
63000	12	87	33
63000	15	231	15
46200	12	12	22
50400	15	14	3
51000	12	180	15
51000	12	315	2
52200	12	29	14
54000	12	7	21
54000	12	38	11
54000	12	113	3
54000	15	18	8
54000	15	359	11
57000	15	36	5
60000	8	320	21
60000	12	24	2
60000	12	32	17
60000	12	49	8
60000	12	56	33
60000	12	252	11
60000	12	272	19
60000	15	25	13
60000	15	36	32
60000	15	56	12
60000	15	64	33
60000	15	108	16
60000	16	46	3
63000	15	72	17
66000	15	64	16
66000	15	84	33
66000	15	216	16
68400	15	42	7
69000	12	175	10
69000	15	132	24
81000	16	55	33

3.  Fit a multiple regression model that relates the salaryto education, work experience, and time spent at the bank so far.  

a - State what your model is.

b - Determine  whether the independent variables are significant, or not, at a level of significance of 5%.

c - Which independent variable is most significant in explaining salary? Which is least significant?

d - Is your overall  model significant? Provide statistical proof by conducting an F-test for overall fit of the regression. State the hypothesis to be tested, the p-value for your F-statistic, and your decision. How much weight of evidence is there in rejecting the null hypothesis?

Answer 1

The regression output for the above data is as follows

There are only some values of the data shown here in the columns C to F becuase there are 94 records and we can't fit them all beside the regression output. But while perfroming the regression analysis, i took all the 93 records of SALARY, EDUC, EXPER and TIME

Question d

The significance for the overall model is tested using the Significane F value from the ANOVA analysis. Significance F value is also the p-value of F-statistic

Here the Significance F value or P-value of F-statistic is 4.80329 * 10-7 in simple terms it is 0.000000048

Our value here is 0.05 which is the default value for any regression analysis if not specified any

If the Significance F value is less than the value, then we can say that the ovreall model is significant

Here the Significance F value of 0.000000048 is way lower than the value of 0.05, hence the overall model is significant

The hypthesis testing is as follows

Null Hypothesis : There is no relationship between salary and education, experiecne and time spend at the bank so far

Alternate Hypothesis : There is relationship between salary and education, experiecne and time spend at the bank so far

Anything we are trying to prove should be our alternate hypothesis, here we are tring to prove that there is relationship between salary and education, experiecne and time spend at the bank so far

The p-value for F-statistic is the Significance F-value which is 0.000000048

The value here is 0.05 which is the default value for any regression analysis if not specified any

value = 1 - confidence level, so the confidence level here is 95%

If the Significance F value is less than the value, then we can say reject the null hypothesis and say that the ovreall model is significant

Here the Significance F value of 0.000000048 is way lower than the value of 0.05, hence we reject the null hypothesis and also the overall model is significant

The smaller the p-value the stronger the weight of evidence in rejecting the null hypothesis

Here our p-value is very very small is 0.000000048, hence there is a very strong weight of evidence in rejecting the null hypothesis