A study was done to look at the relationship between number of vacation days emp

Question

A study was done to look at the relationship between number of vacation days employees take each year and the number of sick days they take each year. The results of the survey are shown below.

A. r =                            [ Select ]                       ["0.0033", "5.373", "-0.0749", "-0.0578"]          

B. r2 =                            [ Select ]                       ["0.0033", "-0.0749", "5.373", "-0.0578"]          

C. Find the equation of the least squares regression line:
y =                            [ Select ]                       ["4.549", "5.373", "-0.5754", "0.0033"]         +                            [ Select ]                       ["-0.0578", "0.0033", "-0.0749", "4.549"]         x

D. What does the regression line predict for the number of sick days an employee took if that person took 11 vacation days that year?                            [ Select ]                       ["5.373", "0.0033", "-0.0578", "4.549"]          (Note that this may not be a reliable prediction. Why?)

E. Test the hypothesis that there is a linear correlation between the number of vacation days and the number of sick days. Use a level of significance of 0.05.

H0: r = 0
Ha: r Not Equal to 0

p-Value =                            [ Select ]                       ["0.0578", "1.265", "0.8377", "0.0033"]          

                           [ Select ]                       ["There is insufficient evidence to support the claim that there is a correlation between the number of vacation days taken and the number of sick days taken.", "There is sufficient evidence to support the claim that there is a correlation between the number of vacation days taken and the number of sick days taken."]      

Vacation 7 12 9 3 8 10 5 8 10 15 12 7 0 9 13 Sick 4 0 12 2 0 9 3 5 1 0 7 8 3 17 0

Explanation / Answer

From Excel

a) r= corrlation coefficient =-0.058

There is a negative correlation between two varaibles

b) r2 =0.003

c) The regression equation is

y=5.37 -0.075 (vacations)

d) when vacations=11

y=5.37-0.075*(11) =4.545

SUMMARY OUTPUT Regression Statistics Multiple R 0.057879 R Square 0.00335 Adjusted R Square -0.07332 Standard Error 5.216426 Observations 15 ANOVA df SS MS F Significance F Regression 1 1.189001 1.189001 0.043695 0.837661 Residual 13 353.7443 27.2111 Total 14 354.9333 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 5.372796 3.342502 1.607418 0.131968 -1.84824 12.59383 -1.84824 12.59383 Vacation -0.07494 0.358491 -0.20903 0.837661 -0.84941 0.699536 -0.84941 0.699536

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