Be sure to use Excel Megastat to solve the following problem . Smoking and short

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).

As understanding of the values and building the skill of reporting data/information, you are asked to interpret the meaning of numerous values.

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?

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 13

Explanation / Answer

Folloiwng is the output of regression analysis generated by Excel Megastat:

1:

The least square regression analysis:

y ' = 7.2865 + 0.1897x

2:

The intercept: When number of Cigarettes smokes is 0, then number of sicks days is approximately 7.3 days.

The slope: When number of Cigarettes is increased by one, then number of sick days incraesed by 0.1897 or 0.2.

3:

The r-sqaure is 0.197. That is 19.7% of the variability in the number of sick days can be explained by knowing the number of cigarettes smoked.

4:

The coefficient of correlation is : 0.444

It shows that relationship between the variables is positive and approxiamtely.

5:

The p-value of F test is 0.0000

Since p-value is less than 0.05 so model is significant.

There is sufficient evidence to conclude that the number of cigarettes smoked is useful in predicting the number of sick days from work.

Regression Analysis r² 0.197 n   231 r   0.444 k   1 Std. Error   3.997 Dep. Var. Days, Y ANOVA table Source SS   df   MS F p-value Regression 896.6419 1   896.6419 56.13 1.46E-12 Residual 3,657.9295 229   15.9735 Total 4,554.5714 230   Regression output confidence interval variables coefficients std. error    t (df=229) p-value 95% lower 95% upper Intercept 7.2865 0.9889 7.369 3.11E-12 5.3381 9.2350 Cigarettes, X 0.1897 0.0253 7.492 1.46E-12 0.1398 0.2396

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