*These questions are from the webbook 'Regression of Stata' of ucla ats. The original questions require to use Stata to answer. Here I try to use SAS to answer these question.*

**Linear Regression**

**Question 1:**Use data set elemapi2. Make five graphs of

**api99**: histogram, kdensity plot, boxplot, symmetry plot and normal quantile plot.

**Answer**

**1**:

1:histogram / kernel density / normal density

2: kernel density

3: boxplot

4: QQ plot

5: normal probability plot

**Question 2:**What is the correlation between

**api99**and

**meals**?

**Answer 2:**

From the output we can see the correlation of api99 and meals is negative, the value is -.908. That is, as the percentage of free meals increase, the api99 value will decrease.

**Question 3:**Regress

**api99**on

**meals**. What does the output tell you?

**Answer 3:**

p-value is < .0001, that is, meals is significant in the regression. the coefficient is negative which means as meals increase by one unit, the value of api99 will decrease by 4.187.

**Question 4:**Create and list the fitted (predicted) values

**Answer 4:**

The first 20 predict values are

**Question 5:**Graph

**meals**and

**api99**with and without the regression line.

**Answer 5:**

With Regression Line:

Without Regression Line (in SAS, with / noline after model statement)

**Question 6:**Look at the correlations among the variables

**api99**

**meals**

**ell**

**avg_ed**using the

**corr**command. Explain how these commands are different. Make a scatterplot matrix for these variables and relate the correlation results to the scatterplot matrix.

**Answer 6:**

Correlation of the variables

Scatter Plot of the variables. It gives virtual representation of the correlation of the variables. api99 is positively correlated with avg_ed and negatively with meals and ell.

**Question 7:**Perform a regression predicting

**api99**from

**meals**and

**ell**. Interpret the output.

**Answer 7:**

From p-value it shows these predictors are significant. Also, it verifies the negative relation of api99 with meals and ell while positive with avg_ed.