Be sure to use Excel Megastat to solve the following problem Smoking and short-t
ID: 3229806 • Letter: B
Question
Be sure to use Excel Megastat to solve the following problem
Smoking and short-term illness case:
Besides the known long-term effects of smoking, some researchers believe that there may be a relationship between the average number of cigarettes smoked and the number of work days missed due to short illnesses. To help understand this, a sample of smokers was drawn. Each person was asked to report the average number of cigarettes smoked per day and the number of days absent from work due to colds last year (sick days).
Answer the following questions:
1. Report the least squares regression equation for predicting the number of sick days as a function of the number of cigarettes smoked.
2. Interpret the practical meaning of the slope of the least squares regression line (1) and the practical meaning of the y-intercept (0). Does the interpretation of 0 make practical sense in the context of this problem/data – why yes/no?
0 (y-intercept) interpretation:
1 (slope) interpretation:
3. What percent of the variability in the number of sick days can be explained by knowing the number of cigarettes smoked?
4. 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.
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?
6. 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.
7. 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.
8. 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.
9. What are the variance and standard deviation of the random errors for this regression analysis?
10. Calculate and report the residual of the 10th observation in the data set.
Cigarettes Days 44 18 41 18 17 18 35 15 33 14 44 15 39 18 35 10 43 16 43 14 41 16 47 19 41 13 30 12 15 18 39 18 36 11 41 13 37 10 43 21 32 13 17 13 34 15 32 11 19 10 44 26 30 13 42 25 34 5 36 8 42 15 47 15 55 19 27 15 28 15 45 22 29 10 37 13 52 13 34 16 48 23 40 15 29 16 34 10 35 19 57 23 48 11 41 10 40 13 36 13 26 7 29 15 52 16 28 16 35 11 42 15 54 19 56 19 37 9 41 17 32 16 63 20 31 15 36 15 31 12 25 15 40 25 55 16 37 21 28 15 56 21 24 16 61 19 40 16 50 14 52 10 45 14 42 19 47 23 22 0 26 12 38 13 46 13 27 9 45 21 43 15 17 11 45 16 40 15 41 17 37 15 30 10 37 14 31 9 49 10 44 15 16 2 25 4 30 5 20 6 36 11 39 14 49 13 37 19 20 11 48 12 28 5 51 16 36 21 42 6 47 9 17 11 22 16 42 21 32 11 31 7 49 16 30 11 31 11 38 18 44 14 41 17 40 20 32 17 48 15 29 17 40 18 45 18 40 15 35 18 37 17 41 16 25 16 35 19 44 15 58 24 27 13 42 22 26 9 48 15 30 11 36 13 26 8 27 6 39 14 17 17 44 21 41 19 26 14 30 14 36 13 31 15 55 17 45 17 27 17 25 9 42 15 18 6 49 15 60 19 40 18 29 15 32 12 35 16 45 15 42 11 52 13 52 16 8 16 36 15 33 12 38 17 38 11 38 14 36 16 44 11 36 14 35 12 30 13 39 21 37 7 26 22 51 18 42 10 44 19 41 15 32 16 56 19 47 22 39 11 18 10 33 12 49 14 16 7 38 9 27 8 26 15 27 8 25 15 14 11 40 9 38 9 38 13 62 18 47 14 54 9 37 6 40 17 56 17 38 16 53 22 52 19 21 11 34 16 23 5 44 13 36 17 45 14 23 10 26 12 54 20 37 19 56 11 38 14 59 18 39 16 38 21 42 20 44 17 32 17 45 13Explanation / Answer
Please note that we can not provide solutions using paid softwares , however we can answer this using excel native functions and no extra software is needed. We simply need to interpret the results
1. Report the least squares regression equation for predicting the number of sick days as a function of the number of cigarettes smoked.
The regression equation is formed using the coefficients column of the output table
Days = 7.2865 + 0.1897* ciggarettes
2. Interpret the practical meaning of the slope of the least squares regression line (1) and the practical meaning of the y-intercept (0). Does the interpretation of 0 make practical sense in the context of this problem/data – why yes/no?
0 (y-intercept) interpretation: The value of Days when the cigarette value is Zero.
1 (slope) interpretation: 0.1897 , this means that for every unit change in the value of the cigarettes , the days would change by a factor of 0.1897 units
3. What percent of the variability in the number of sick days can be explained by knowing the number of cigarettes smoked?
This is r square value , which is 0.197 . This means that model is able to explain only 19.7% variation of the data . Higher the value of r2 better the model. The value ranges from 0 to 1
4. 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.
The r value is 0.444 , as can be seen from the regression table. This means that there is a weak positive correlation between days and cigarette variable. The same value can also be calculated by taking square root of r2 value as sqrt(0.197) = 0.444.
As the value is positive , hence we say that there is a weak positive correlation between the dependent and the independent variable.
Note that correlation value can range from -1 to 1 . The values on the extreme ends are high correlations and the values close to zero means no or little correlation
Please note that we can answer only 4 subparts of a question at a time , as per the answering guidelines
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