Now it's your turn. Use the the skin cancer dataset (csv) to obtain the following output.

Fit the linear regression model

$$MORT=\beta_0+\beta_1*Lat+\beta_2*Long+\beta_{12}Lat*Long+\varepsilon_i$$

Obtain the confidence intervals for the regression parameters (the $\beta$'s).
Create a plot of the residuals vs the fitted values.
Create a histogram and QQ plot of the residuals.
Calculate the confidence interval for the mean mortality rate and the prediction interval when Lat = 33 and Long = 86.
Fit the reduced regression model without the interaction term.

Questions 1-4 can be answered by using PROC REG with the CLB option in the MODEL statement. We will first need to calculate the product of Lat and Long for the interaction term.

LIBNAME Survey "H:\BiostatCourses\PHC6937SurveryBiostat\Lectures\MLR\Data";

PROC IMPORT datafile="H:\BiostatCourses\PHC6937SurveryBiostat\Lectures\MLR\Data\skincancer.csv"
out=Survey.cancer dbms=csv replace;
getnames=Yes;
RUN;

DATA cancer_temp;
SET survey.cancer;
LatLong = Lat*Long;
RUN;

PROC REG DATA=cancer_temp;
MODEL Mort = Lat Long LatLong / CLB;
RUN;

For number 5, we need to add a row to the dataset with a missing value for Mort so we can use the output statement to get the confidence and prediction intervals.

DATA cancer_temp2;
INPUT Mort Lat Long LatLong;
DATALINES;
. 33 86 2838
;
RUN;

DATA cancer_temp;
SET cancer_temp cancer_temp2;
RUN;

ODS SELECT NONE;
PROC REG DATA=cancer_temp;
MODEL Mort = Lat Long LatLong / CLB;
OUTPUT OUT=pred(where=(Mort=.)) p=predicted lcl=UCL_Pred ucl=LCL_Pred 
LCLM=LCLM_Pred UCLM=UCLM_Pred;
RUN;
ODS SELECT ALL;

PROC PRINT DATA=pred;
VAR LAT LONG LATLONG predicted LCLM_Pred UCLM_Pred UCL_Pred LCL_Pred;
RUN;

For number 6, we need to run PROC REG again without the interaction term in the model statement.

PROC REG DATA=Survey.cancer;
MODEL Mort = Lat Long / CLB;
RUN;

Number of Observations Read	49
Number of Observations Used	49

Analysis of Variance
Source	DF	Sum of Squares	Mean Square	F Value	Pr > F
Model	3	36778	12259	32.72	<.0001
Error	45	16860	374.65766
Corrected Total	48	53637

Root MSE	19.35608	R-Square	0.6857
Dependent Mean	152.87755	Adj R-Sq	0.6647
Coeff Var	12.66116

Parameter Estimates
Variable	DF	Parameter Estimate	Standard Error	t Value	Pr > \|t\|	95% Confidence Limits
Intercept	1	489.37255	185.66083	2.64	0.0115	115.43245	863.31265
Lat	1	-8.08381	4.49542	-1.80	0.0789	-17.13804	0.97043
Long	1	-1.10396	1.98941	-0.55	0.5817	-5.11084	2.90293
LatLong	1	0.02318	0.04794	0.48	0.6312	-0.07339	0.11974

Number of Observations Read	49
Number of Observations Used	49

SAS Output

The REG Procedure

MODEL1

Fit

Mort

Number of Observations

Analysis of Variance

Fit Statistics

Parameter Estimates

Observation-wise Statistics

Mort

Diagnostic Plots

Fit Diagnostics

Residual Plots

Panel 1

SAS Output

The PRINT Procedure

Data Set WORK.PRED

SAS Output

The REG Procedure

MODEL1

Fit

Mort

Number of Observations

Analysis of Variance

Fit Statistics

Parameter Estimates

Observation-wise Statistics

Mort

Diagnostic Plots

Fit Diagnostics

Residual Plots

Panel 1

Root MSE	19.19417	R-Square	0.6840
Dependent Mean	152.87755	Adj R-Sq	0.6703
Coeff Var	12.55525