(0.5) What percent of the variability in the number of sick days can be explaine
ID: 3258809 • Letter: #
Question
(0.5) What percent of the variability in the number of sick days can be explained by knowing the number of cigarettes smoked?
(0.5) Calculate the coefficient of correlation between the independent and dependent variables. Comment on what the magnitude and direction of this correlation coefficient says about the linear relationship between the independent and dependent variables.
(0.5) Using a significance level of = .05, is there sufficient evidence to conclude that the number of cigarettes smoked is useful in predicting the number of sick days from work?
d. (0.5) Estimate with 95% confidence the average number of sick days for all individuals who smoke 30 cigarettes per day. Interpret the practical meaning of this interval estimate in the context of the problem.
e.(0.5) Predict with 95% confidence the number of sick days of a single individual who smokes 30 cigarettes per day. Interpret the practical meaning of this interval estimate in the context of the problem.
f.0.5) Estimate the true population slope for this least squares regression line with 95% confidence. Interpret the practical meaning of this interval estimate in the context of the problem.
(0.5) What are the variance and standard deviation of the random errors for this regression analysis?
(0.5) Calculate and report the residual of the 10th observation in the data set.
SUMMARY OUTPUT Regression Statistics Multiple R 0.443696244 R Square 0.196866357 Adjusted R Square 0.193359224 Standard Error 3.996685058 Observations 231 ANOVA df SS MS F Significance F Regression 1 896.6418865 896.6418865 56.13311838 1.46321E-12 Residual 229 3657.929542 15.97349145 Total 230 4554.571429 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% DAYS 7.286531113 0.988867818 7.368559259 3.10726E-12 5.338088429 9.234973797 5.338088429 9.234973797 # OF CIGS 0.189742532 0.02532533 7.49220384 1.46321E-12 0.139842078 0.239642986 0.139842078 0.239642986Explanation / Answer
a] here R square = 0.196866
19.69% of the variability in the number of sick days can be explained by knowing the number of cigarettes smoked.
b] Multiple R = 0.443696
the coefficient of correlation between the independent and dependent variables is 0.4437. There is a positive correlation between independent and dependent variables. and both these variables goes in same direction. that is if one increase the other also increase and vise versa.
c]
Using a significance level of = 0.05, is there sufficient evidence to conclude that the number of cigarettes smoked is useful in predicting the number of sick days from work. Because the corresponding p-value of days is very very small ( 3.10726E-12) compared with = 0.05. Hence we reject null hypothesis.
d]
95% confidence the average number of sick days for all individuals who smoke 30 cigarettes per day.
( 5.338088429, 9.234973797 ) near about ( 5 , 9).
there is a 95% chances of who smoke 30 cigarettes per day will be sick for an average 5 to 9 days.
e] same as part d] because both the cases their 95% confidence interval is same.
f] variance of random error = 15.97 and standard deviation of random error is = 3.99
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