Question

Let us instead fit a linear regression model to the data on employee sales. in particular, we fit the model: sales = b0 + b1*employee group + e, where employee group is a categorical variable with values a, b, and c. we set group a to be the reference category.  from this model we get the following output. from this output,

1. what can we conclude is the mean sales for group a (in dollars/day)?

2.what can you conclude is the difference in mean sales for group B compared to group A?

3.what can we conclude is the average sales for group C?

4.We sat group A to be the reference category. find out whether the difference in average daily sales between between Group A and B is statistically significant. what is the t-value for group B?

5.Next, we fit the following linear regression model : Sales= B0+B1*Age+e. Where age is in year and sales is in $/day. the model gives a parameter estimate, B1=2, with p<0.0001. How would we interpret the parameter estimate.

For every 1 year______in age, there is a corresponding __________ $/day ________.

coefficient estimate standard error t-test p-value

intercept 100 10

employee group b 10 5  

employee group c -20 5

Answer 1

The estimated regression equation is :

For group A, :sales = 100

For group B, sales = 100 + 10 = 110

For group C, sales = 100 -20  = 80

1. The mean sales for group a (in dollars/day) = 100

2. The difference in mean sales for group B compared to group A= 110 - 100 = 10

3. The the average sales for group C = 80

4. t-value for group B = estimated slope / standard error = 10/5 = 2

5. For every 1 year increase in age, there is a corresponding 2 $/day increase in sales.