Unit V Scholarly Activity
MAMA0611
UnitVScholarlyActivity-Professorcomments..pdf
Unit V – Scholarly Activity – Correlation and Regression Analysis 2
Correlation and Regression Analysis Using Sun Coast Data Set
Correlation
The correlation is as follows;
0 2 4 6 8 10 12 0
2
4
6
8
10
12
14
f(x) = − 0.522376553687661 x + 10.0814448333379 R² = 0.512633353670829
mean annual sick days per employee
microns
M e
a n
a n
n u
a l
si ck
d a
y s
p er
e m
p lo
y e
e
As the microns increases, the mean annual sick days per employee reduces. The gradient is
-0.5224.
Regression
Carrying out regression has the following output;
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.939559324
R Square 0.882771723
Adjusted R Square 0.882241279
Standard Error 24.61328875
Observations 223
Unit V – Scholarly Activity – Correlation and Regression Analysis 3
Coefficients Standar d Error t Stat P-value
Lower 95%
Upper 95%
Lower 95.0%
Upper 95.0%
Intercept 273.449419 2.66526
2 102.597
6 2.1E-
188 268.196
8 278.70
2 268.196
8 278.70
2
X1 -0.143367741 0.00351
4 -40.7947 7.7E-
105 -0.15029
- 0.1364
4 -0.15029
- 0.1364
4
From the table above, it can be concluded that the equation is y= - 0.1433x + 273.45.
Additionally, since the regression was carried out at the 95% confidence interval, there is a good
relationship between the lost hours and the safety training expenditure not a coincidental since the
p value is 7.7E-105 (Illowsky, Dean, & Illowsky, 2017).
The residues are as follows;
RESIDUAL OUTPUT
Observation Predicted Y Residuals Standard Residuals
1 -11.15260858 21.15261 0.86134
2 58.39780679 -28.3978 -1.15637
3 111.9512496 -71.9512 -2.92987
4 87.91736812 -47.9174 -1.95121
5 66.20231653 -26.2023 -1.06697
6 113.9571076 -63.9571 -2.60435
7 26.74134927 33.25865 1.354301
8 16.87005017 43.12995 1.756263
9 10.00890017 49.9911 2.035651
10 -13.28606394 73.28606 2.984229
11 -52.26201813 112.262 4.57134
12 57.25487916 12.74512 0.518985
13 52.32919366 17.67081 0.71956
14 51.96073857 18.03926 0.734564
15 51.63672747 18.36327 0.747758
16 48.71360259 21.2864 0.866788
17 44.06103265 25.93897 1.056242
18 65.18067801 14.81932 0.603447
Unit V – Scholarly Activity – Correlation and Regression Analysis 4
Multi-Regression
The output are as follows;
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.60184
2
R Square 0.36221
4
Adjusted R Square
0.36008 3
Standard Error 5.51856
6
Observations 1503
ANOVA
df SS MS F Significanc
e F
Regressio n 5
25891.8 9
5178.37 8
170.036 1 2.1E-143
Residual 1497 45590.4
9 30.4545
7
Total 1502 71482.3
8
Coefficients Standard Error t Stat P-value
Lower 95%
Upper 95%
Lower 95.0%
Upper 95.0%
Intercept 126.8225 0.62382 203.299
7 0 125.598
8 128.046
1 125.598
8 128.046
1
X 1 -0.00112 4.76E-05 -23.4885 4.1E-104 -0.00121 -0.00102 -0.00121 -0.00102
X 2 0.047342 0.03730
8 1.26895
7 0.20465
4 -0.02584 0.12052
4 -0.02584 0.12052
4
X 3 -5.49532 2.92796
2 -1.87684 0.06073
4 -11.2387 0.24802
6 -11.2387 0.24802
6
Unit V – Scholarly Activity – Correlation and Regression Analysis 5
X 4 0.08324 0.0093 8.95031
7 1.02E-18 0.06499
7 0.10148
2 0.06499
7 0.10148
2
X 5 -240.506 16.5190
3 -14.5593 5.21E-45 -272.909 -208.103 -272.909 -208.103
From the immediate above table, the y variable was the decibel. The equation from the
above table is as follows;
Y=-0.00112x1 + 0.04734 x2 – 5.495x3 + 0.08324 x4 – 240.506 x5 + 126
The Independent T-test
The results are as follows;
t-Test: Paired Two Sample for Means
Variable 1
Variable 2
Mean 69.7903 2
84.7741 9
Variance 122.004 5
26.9645 7
Observations 62 62
Pearson Correlation 0.06032 5
Hypothesized Mean Difference
0
df 61
t Stat -9.89922
P(T<=t) one-tail 1.31E-14
t Critical one-tail 1.67021 9
P(T<=t) two-tail 2.62E-14
t Critical two-tail 1.99962 4
Given the 95% confidence interval was used, one tailed test shows relationship between the
variables because the p-value was 1.31E-14.
Unit V – Scholarly Activity – Correlation and Regression Analysis 6
Paired Sample
The analysis results are as follows;
t-Test: Paired Two Sample for Means
Variable 1
Variable 2
Mean 32.8571 4
33.2857 1
Variance 150.458 3
155.5
Observations 49 49
Pearson Correlation 0.99223 6
Hypothesized Mean Difference
0
df 48
t Stat -1.9298
P(T<=t) one-tail 0.02977 6
t Critical one-tail 1.67722 4
P(T<=t) two-tail 0.05955 3
t Critical two-tail 2.01063 5
There is a relationship between the two variable given since the p value is 0.029 which less
than 0.05.
Unit V – Scholarly Activity – Correlation and Regression Analysis 7
References
Illowsky, B., Dean, S. L., & Illowsky, B. (2017). Introductory statistics.
