Question

X: Day of Leave Used	3	3	2	1	4	5	4	3	6	5
Y: Performance score	12	13	11	12	12	11	14	13	12	12

a) Using the table given above; Correlation (Relationship) Coefficient and Specification
Calculate the coefficient and interpret briefly? 25 POINTS
b) Provide brief information about the direction of the correlation (relationship)?

Answer 1

correlation coefficient r = 0.123

There is a weak positive linear relationship between x and y variables.

The strenght and direction of the x and y variables are weak positive

E4 Х =CORREL(A1:A11, B1:B11) Private Public D E F 4 correlation coefficient r = 0.123 N 01 Business Business Unrestricted A B с 1 X у 2 3 12 3 3 13 2 11 1 12 6 12 7 8 5 14 9 13 10 6 11 5 12 13 11 UT O W 01 07 A 12 12

Run a regression analysis in excel followed by below procedures:

1. Go to data tab --> data analysis --> choose Regression

Get & Transform Data Queries & Connections Data Types Sort & Filter D14 fx Regression ? Х Input Input Y Range: OK $B$1:$B$11 1 Cancel 0 Business Business Unrestricted Input X Range: $A$1:$A$11 1 A B C D Help Labels Constant is Zero у Confidence Level: 95 %6 3 3 2 Output options $G$3 1 4 1 x 2 3 4 5 6 7 8 9 10 11 12 13 12 13 11 12 12 11 14 13 12 12 5 5 3 O Qutput Range: New Worksheet Ply: O New Workbook Residuals Residuals Standardized Residuals Residual Plots Line Fit Plots 6 5 Normal Probability Normal Probability Plots

А B с D E F G H - J K L M N o Р X у 1 2 3 4 3 3 SUMMARY OUTPUT 2 5 1 12 13 11 12 12 11 14 13 12 12 Regression Statistics Multiple R 4 R Square 5 5 3 6 Adjusted R Square Standard Error Observations 0.123 0.015 -0.108 0.967 10 5 ANOVA df 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 Significance F 0.73 Regression Residual Total SS MS F 1 0.115837 0.115837 0.123821 8 7.484163 0.93552 9 7.6 Intercept х Coefficients andard Ern t Stat P-value 11.932 0.820406 14.54417 4.89E-07 0.072 0.205746 0.351882 0.734016 Lower 95% Upper 95%ower 95.0%pper 95.0% 10.04026611 13.82399 10.04027 13.82399 -0.402051937 0.546848 -0.40205 0.546848

Regression equation:

Coefficients:

y = 11.932 + 0.072 x

P-value = 0.73

If the p-value is NOT less than the significance level (α>0.05)

• Decision: DO NOT REJECT the null hypothesis.
• Conclusion: "There is insufficient evidence to conclude that there is a significant linear relationship between x and y because the correlation coefficient is NOT significantly different from zero."