3. Corona Industries (Ch 13 Regression) Corona Industries is a large software en
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Question
3. Corona Industries (Ch 13 Regression)
Corona Industries is a large software engineering company, offering its clients the highest standards in innovative technology solutions and reliable support. About 25% of the employees at Corona Industries are programmers. Corona frequently hires entry level programmers without significant programming experience or programming references. Some of these programmers work out well and some don’t. The human resources department has suggested that the company consider using the Standardized Test of Programming Aptitude (STPA), a standardized test designed to measure aptitude for computer programming, to screen applicants for the programming positions.
In order to assess the STPA as a predictor of future job performance, 30 recent applicants were tested using the STPA. All were hired, regardless of their STPA score. At a later date, managers were asked to rate the quality of the job performance of these 30 employees, using a 1 to 10 rating scale (where 1= very low and 10 =very high). Factors considered in the rating included the employee’s ability to implement business logic in code, bug rate, and overall contribution to the programming team. The file Corona_STPA.xlsx contains the STPA scores and job performance ratings (Ratings) for the 30 employees.
Assess the significance and importance of the STPA score as a predictor of job performance. Make sure to address both practical and statistical significance. Defend your answer using relevant results from the regression analysis.
Based on the regression results, how would you quantify the relationship between STPA score and job performance rating?
Predict the mean job performance rating for all employees with a STPA score of 6. Do you have any concerns using the regression model for predicting mean job performance rating given the STPA score of 6?
DATA:
STPA Score Performance Rating 10 5 35 7 27 7 19 6 38 8 24 6 34 7 17 4 16 7 33 6 37 7 26 6 23 8 20 5 24 6 31 7 32 5 25 6 32 8 9 6 25 6 12 4 20 7 13 4 21 5 23 5 32 8 24 7 26 7 25 4Explanation / Answer
Result:
Assess the significance and importance of the STPA score as a predictor of job performance. Make sure to address both practical and statistical significance. Defend your answer using relevant results from the regression analysis.
Calculated F=13.40, P=0.0010 which is < 0.05 level of significance. The regression model is significant and good. STPA score is useful in predicting Performance Rating.
Regression Analysis
r²
0.324
n
30
r
0.569
k
1
Std. Error
1.048
Dep. Var.
Performance Rating
ANOVA table
Source
SS
df
MS
F
p-value
Regression
14.7150
1
14.7150
13.40
.0010
Residual
30.7517
28
1.0983
Total
45.4667
29
Regression output
confidence interval
variables
coefficients
std. error
t (df=28)
p-value
95% lower
95% upper
Intercept
3.9176
0.6348
6.171
1.16E-06
2.6172
5.2180
STPA Score
0.0907
0.0248
3.660
.0010
0.0399
0.1414
Predicted values for: Performance Rating
95% Confidence Interval
95% Prediction Interval
STPA Score
Predicted
lower
upper
lower
upper
Leverage
6
4.462
3.447
5.476
2.087
6.836
0.223
Based on the regression results, how would you quantify the relationship between STPA score and job performance rating?
Performance Rating = 3.9176+0.0907*STPA score
Predict the mean job performance rating for all employees with a STPA score of 6. Do you have any concerns using the regression model for predicting mean job performance rating given the STPA score of 6?
For STPA score of 6,
Predicted Performance Rating = 3.9176+0.0907*6
=4.462
Since STPA score of 6 not in the range of observed data, prediction is not appropriate for 6.
Regression Analysis
r²
0.324
n
30
r
0.569
k
1
Std. Error
1.048
Dep. Var.
Performance Rating
ANOVA table
Source
SS
df
MS
F
p-value
Regression
14.7150
1
14.7150
13.40
.0010
Residual
30.7517
28
1.0983
Total
45.4667
29
Regression output
confidence interval
variables
coefficients
std. error
t (df=28)
p-value
95% lower
95% upper
Intercept
3.9176
0.6348
6.171
1.16E-06
2.6172
5.2180
STPA Score
0.0907
0.0248
3.660
.0010
0.0399
0.1414
Predicted values for: Performance Rating
95% Confidence Interval
95% Prediction Interval
STPA Score
Predicted
lower
upper
lower
upper
Leverage
6
4.462
3.447
5.476
2.087
6.836
0.223
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