Question

A human resources director believes that increased physical activity of the employee will results in fewer hours lost to illness. To test this hypothesis she randomly sampled 10 individuals from her company. Each employee was asked 2 simple questions: 1) How many hours per week do exercise? ; 2) How many work hours per year do you lose due to illness? The following results were obtained:

Number of hours/week exercise	Number of work hours/year lost to illness
3	76
3	71
4	70
5	74
6	63
7	51
7	75
8	67
8	40
9	63

NOTE: The correlation coefficient, r, which is -0.56, the mean (M) and standard deviation (SD) for exercise (6 and 2.16 respectively), and the M and SD for illness (65 and 11.53 respectively).

1. Fill in the table below

Source	SS	df	MS	F
Model	Answer	Answer	Answer	Answer
Residual	Answer	Answer	Answer
Total	Answer

Is your model a significant fit of the data (quote the relevant statistics)?

AnswerNoYes, model is Answernot a significanta significant fit of the data, F(Answer, Answer) = Answer, p Answer><.05.

How much of the variance in work hours lost to illness can be explained by exercise? Answer% Is it significant? AnswerNoYes

What is the power of the study? Answer

Write out the regression equation for the model: Y = Answer+AnswerX. If the individual spends 10 per week exercising what would be the predicted number of works hours lost to illness? Answer

If the predictor value decreases by 1.5 standard deviations, how much would your outcome variable change (raw score units)? Answer

What is the standard error of the estimate? Answer

What is the standard error for testing significance of the slope? Answer

Figure the confidence interval (95%). Lower Answer Upper Answer

Answer 1

This is the dataset and its mean and std dev.

The correlation coefficient is equal to

First, we create the regression output for the data.

b)

Is your model a significant fit of the data (quote the relevant statistics)?

The significance level of the linear model is equal to 0.0907 > 0.05. Which means that this model is not significant for the data.

c)

How much of the variance in work hours lost to illness can be explained by exercise?

31% variance in work hours lost to illness can be explained by exercise. This is shown by the R-squared statistic.

d)

The regression model is given by the equation

Y=83-3(x)

Y=Number of work hours/year lost to illness

x=Number of hours/week exercise

If the individual spends 10 hrs per week exercising, what would be the predicted number of works hours lost to illness?

$\\Y=83-3(10)\\ Y=53$