Question 2 Suppose a researcher gathered survey data from 19 employees and asked the employees to rate their job satisfaction on a scale from 0 to 100 (with 100 being perfectly satisfied). Suppose the following data represent the results of this survey. Assume that relationship with their supervisor is rated on a scale from 0 to 50 (0 represents a poor relationship and 50 represents an excellent relationship); overall quality of the work environment is rated on a scale from 0 to 100 (0 represents poor work environment and 100 represents an excellent work environment); and opportunities for GB513: Business Analytics 2 of 4 advancement is rated on a scale from 0 to 100 (0 represents no opportunities and 100 represents excellent opportunities). Answer the following questions: a) What is the regression formula based on the results from your regression? b) How reliable do you think the estimates will be based on this formula? Explain your answer by citing the relevant metrics. c) Are there any variables that do not appear to be good predictors of job satisfaction? How can you tell? d) If a new employee reports that her relationship with her supervisor is 40, rates her opportunities for advancement to be at 30, finds the quality of the work environment to be at 75, and works 60 hours per week, what would you expect her job satisfaction score to be? Job satisfaction Relationship with supervisor Opportunities for advancement Overall quality of work environment Total hours worked per week 55 27 42 50 52 20 35 28 60 60 85 40 7 45 42 65 35 48 65 53 45 29 32 40 58 70 42 41 50 48 35 22 18 75 55 60 34 32 40 50 95 40 48 45 40 65 33 11 60 38 85 38 33 55 47 10 5 21 50 62 75 37 42 45 43 80 37 46 40 42 50 31 48 60 46 90 42 30 55 38 75 36 39 70 43 45 20 22 40 42 65 32 12 55 53
can the answer be typed out please with excel?
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Regression Statistics | |||||||||
Multiple R | 0.906974193 | ||||||||
R Square | 0.822602186 | ||||||||
Adjusted R Square | 0.771917097 | ||||||||
Standard Error | 11.05943598 | ||||||||
Observations | 19 | ||||||||
ANOVA | |||||||||
df | SS | MS | F | Significance F | |||||
Regression | 4 | 7940.275841 | 1985.06896 | 16.22966819 | 3.73654E-05 | ||||
Residual | 14 | 1712.355738 | 122.3111241 | ||||||
Total | 18 | 9652.631579 | |||||||
Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | ||
Intercept | 98.32908724 | 29.9636493 | 3.281612539 | 0.005458373 | 34.0634513 | 162.5947232 | 34.0634513 | 162.5947232 | |
Relationship with supervisor(X1) | 1.323243881 | 0.368701564 | 3.58892939 | 0.002962862 | 0.532457676 | 2.114030086 | 0.532457676 | 2.114030086 | |
Opportunities for advancement(X2) | 0.077349313 | 0.207254871 | 0.373208663 | 0.714583336 | -0.367168174 | 0.5218668 | -0.367168174 | 0.5218668 | |
Overall quality of work environment(X3) | -0.170042037 | 0.25373087 | -0.670166926 | 0.513654675 | -0.714240629 | 0.374156554 | -0.714240629 | 0.374156554 | |
Total hours worked per week(X4) | -1.522385082 | 0.433602894 | -3.511012271 | 0.003458686 | -2.452370794 | -0.59239937 | -2.452370794 | -0.59239937 |
a) the regression formula based on the results from your regression
Y = 98.329 + 1.323 X1 + 0.077 X2 - 0.17 X3 - 1.522 X4
b)
R = 0.90697 = 90.7%
Which means There is statistical strong relation between dependent and independent variables
Another way
H0 : There is no statistically significant relation between dependent and independent variables
Ha : There is statistically significant relation between dependent and independent variables
P value = 0 , reject H0
There is statistically significant relation between dependent and independent variables
c)
Coefficient Table Iteration 1 (adjusted R-squared = 0.772)
Coeff |
SE | t-stat | lower t0.025(14) | upper t0.975(14) |
Stand Coeff |
p-value |
VIF |
|
---|---|---|---|---|---|---|---|---|
b | 98.3291 | 29.9636 | 3.2816 | 34.0635 | 162.5947 | 0.000 | 0.005458 | |
X1 | 1.3232 | 0.3687 | 3.5889 | 0.5325 | 2.1140 | 0.5143 | 0.002963 | 1.6209 |
X2 | 0.07735 | 0.2073 | 0.3732 | -0.3672 | 0.5219 | 0.04450 | 0.7146 | 1.1219 |
X3 | -0.1700 | 0.2537 | -0.6702 | -0.7142 | 0.3742 | -0.07679 | 0.5137 | 1.0361 |
X4 | -1.5224 | 0.4336 | -3.5110 | -2.4524 | -0.5924 | -0.4866 | 0.003459 | 1.5156 |
Coefficient Table
Iteration 2 (adjusted R-squared = 0.785)
Coeff |
SE | t-stat | lower t0.025(15) | upper t0.975(15) |
Stand Coeff |
p-value |
VIF |
|
---|---|---|---|---|---|---|---|---|
b | 98.9633 | 29.0445 | 3.4073 | 37.0565 | 160.8701 | 0.000 | 0.003899 | |
X1 | 1.3661 | 0.3402 | 4.0160 | 0.6411 | 2.0911 | 0.5310 | 0.001122 | 1.4637 |
X3 | -0.1781 | 0.2454 | -0.7257 | -0.7013 | 0.3450 | -0.08044 | 0.4792 | 1.0286 |
X4 | -1.5048 | 0.4185 | -3.5958 | -2.3967 | -0.6128 | -0.4809 | 0.002648 | 1.4976 |
Coefficient Table
Iteration 3 (adjusted R-squared = 0.791)
Coeff |
SE | t-stat | lower t0.025(16) | upper t0.975(16) |
Stand Coeff |
p-value |
VIF |
|
---|---|---|---|---|---|---|---|---|
b | 92.4738 | 27.2217 | 3.3971 | 34.7663 | 150.1814 | 0.000 | 0.003683 | |
X1 | 1.3504 | 0.3344 | 4.0381 | 0.6415 | 2.0593 | 0.5249 | 0.0009526 | 1.4578 |
X4 | -1.5543 | 0.4067 | -3.8215 | -2.4165 | -0.6921 | -0.4968 | 0.001503 | 1.4578 |
X2,X3 are not good predictors of job satisfaction
d) If a new employee reports that her relationship with her supervisor is 40, rates her opportunities for advancement to be at 30, finds the quality of the work environment to be at 75, and works 60 hours per week
Y = 98.329 + 1.323 X1 + 0.077 X2 - 0.17 X3 - 1.522 X4
Y = 98.329 + 1.323 *40 + 0.077 *30 - 0.17 *75 - 1.522 * 60
Y = 98.329 + 52.92 + 2.31 - 12.75 - 91.32
= 153.559 - 104.07
Y = 49.489
Job satisfaction = 49.49
Question 2 Suppose a researcher gathered survey data from 19 employees and asked the employees to rate their job satisfaction on a scale from 0 to 100 (with 100 being perfectly satisfied). Suppose the...
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