$4-35$ points

On the supporting document and data file, there is information about some magazine$$s pronouncement of the $100$ best companies to work for. Our interest in the data is understanding the variable Salaried $($the Y variable$).$

Model $1$

In the first model you consider a simple linear regression and use as the independent variable the Hourly variable.

What is your idea about the expected numerical sign of the hourly variable?

I think it will be positive

State the null and alternative hypothesis about the beta for the hourly variable.

Obtain the regression results.

What is the estimated coefficient?

Write a sentence explaining the interpretation of this number for the estimated coefficient.

What is the t$-$stat for the coefficient?

What is the p$-$value for the coefficient?

What is your conclusion about the hypothesis test?

What is the value of the adjusted R Square and what does this number mean in this specific context? $($Note you gave me the general definition above. I want the interpretation as related to this problem.

Model $2$

In the second model you will add information about the size of the company as additional independent variables.

There are three ways to do this:

$3$ create dummy variables for small and large $.$

Obtain the regression results for the new model and include a $90\%$ confidence interval.

In this model what is the value of the F statistic, what is being tested with the statistic, and what do you conclude from the test?

With these added variables, does you view about the Hourly variable change from what you found in the first model? Why or why not based on the regression information?

Interpret the coefficients on each of the dummy variables and comment on what the p$-$value of each means.

What is the interpretation of the $90\%$ confidence interval on the $$larger$$ of the two sizes in your model?

What is the value of the adjusted R Square and when you compare this to the value in the previous model what do you conclude about the inclusion of the additional variables in the second model?