Understanding Advanced SAS Procedures

Master advanced statistical modeling in SAS with our detailed question-and-answer guide. This Understanding Advanced SAS Procedures post explains the core statements and functionality of essential SAS procedures like PROC NLIN for nonlinear regression, PROC NLMIXED for nonlinear mixed models, PROC GLIMMIX for linear and generalized linear mixed models, and PROC PROBIT for dose-response analysis. Learn how to use PARMS, MODEL, RANDOM, and CLASS statements correctly, avoid common syntax errors, and interpret your results with practical examples from the sashelp.cars and sashelp.iris datasets. Perfect for data analysts and statisticians looking to deepen their SAS programming skills.

Understanding Advanced SAS Procedures

Understanding Advanced SAS Procedures

Explain the following SAS Statements used in the Example below (Non-Linear Mixed Model)

proc nlmixed data = CARS;
parms b1 = 220 b2 = 500 b3 = 310 s2u = 100 s2e = 60;
model X ~ normal(num/den, s2e);
random u1 ~ normal(0, s2u) subject = NUMBER;
run;

This is an excellent example of a nonlinear mixed model in SAS. The MIXED MODEL statement defines the dependent variable and its conditional distribution given the random effects. In the above statement, a normal (Gaussian) conditional distribution is specified.

This code is fitting a nonlinear mixed-effects model to data about cars (from the CARS dataset). It is trying to estimate parameters ($b_1, b_2$, and $b_3$) for a specific nonlinear relationship between a predictor and the outcome $X$, while also accounting for random variations between different groups of cars (grouped by NUMBER).

The RANDOM statement defines the single random effect to be $u1$, and specifies that it follows a normal distribution with mean $0$ and variance $s2u$. The SUBJECT= statement in the RANDOM statement is used to define a variable that will indicate when the random effect obtains new realizations.

Explain the following SAS statements (Linear Mixed Model) in the example below

proc glimmix data = sashelp.iris;
class species;
model age = weight;
random age = weight;
run;

The CLASS statement instructs the technique to treat the variable species as type variables. The version announcement in the example shown above specifies the reaction variable as a pattern proportion by means of the use of the occasions/trials approach.

This PROC GLIMMIX code contains a critical error in its RANDOM statement, which makes the model, as written, invalid and nonsensical.

In code, it is trying to fit a linear mixed model to the sashelp.iris dataset (famous Fisher’s Iris data). The intent might have been to see how age (which does not exist in the standard iris dataset) is related to weight (which also does not exist), while accounting for the grouping structure of species. The syntax of the RANDOM statement is completely incorrect.

Explain the use of each SAS statement (PROC PROBIT) given below

PROC PROBIT dataset;
CLASS <dependent variables>;
Model < dependent variables > = <independent VARIABLES>;

This statement outlines the basic structure for using PROC PROBIT in SAS, but it contains a few common misunderstandings and a critical error in the CLASS statement. However, the line-by-line explanation of the code is:

The DATA= option specifies the dataset that will be studied.

The PLOTS= choice within the PROC PROBIT statement, collectively with the ODS graphics announcement, requests all plots (as all have been specified in brackets, we will pick out a selected plot also) for the anticipated opportunity values and peak ranges.

The model statement prepares a response between a structured variable and independent variables. The variables top and weight are the stimuli or explanatory variables.

Explain the following SAS example (PROC NLIN)

proc nlin data = sashelp.cars method = gauss;
parms hosepower = 135
cylinders = 6;
model mpg_highway = (horsepower/cylinders);
run;

This code is used to fit a nonlinear regression model (PROC NLIN) to car data. The METHOD = option directs PROC NLIN to use the GAUSS iterative method. The PARMS statement declares the parameters and specifies their initial values.

The code is trying to model a car’s highway fuel efficiency (mpg_highway) as a simple nonlinear function of its power (horsepower) and engine size (cylinders). Specifically, it is testing the hypothesis that highway MPG is directly proportional to the power-per-cylinder (horsepower / cylinders). The code contains a critical error in its model specification, which will cause it to fail.

R Frequently Asked Questions

Regression Correlation MCQs 14

Master the fundamentals of statistical relationships with this comprehensive 20-question Multiple Choice Quiz on Regression Correlation MCQs. Designed for students, researchers, data analysts, and aspiring data scientists, this quiz tests your understanding of key concepts essential for exams and job interviews. Challenge yourself with problems on finding regression equations, correlation coefficients, means, standard deviations, covariance, and the coefficient of determination. Perfect your skills in interpreting data and predicting values to solidify your grasp on these critical statistical techniques. Let us start with the Regression Correlation MCQs now.

Online Regression Correlation MCQs with Answers

Online MCQs about Correlation and Regression Analysis

1. Two given regression equations are $2X+3Y=5$ and $x+2Y=4$, then equation of the $Y$ on $X$ is

 
 
 
 

2. For the two variables, the regression of $Y$ on $X$ is $4X-5Y-90=0$ and the regression equation of $X$ on $Y$ is $X+kY-6=0$. If the coefficient of determination is 0.48, then the value of $k$ is

 
 
 
 

3. The value of $a_{xy}$ in the regression equation $2X+3Y+50=0$ is

 
 
 
 

4. The value of $b_{yx}$ in the regression equation $2X + 3Y +50 =0$ is

 
 
 
 

5. Given that $r=0.8$, $\Sigma XY = 60$, $\delta_Y = 2.5$, $\Sigma X^2=90$, where $X$ and $Y$ are the deviations from their respective means, then the value of $n$ is

 
 
 
 

6. The statement “two regression lines always intersect at the mean value of $X$ and $Y$” is

 
 
 
 

7. The covariance between variables $X$ and $Y$ of five items is 6, and their standard deviations are 2.45 and 2.6, respectively. What is the value of $r$?

 
 
 
 

8. If $r=0.6$, then the coefficient of non-determination is

 
 
 
 

9. The regression coefficients are equal to zero if $r$ is equal to

 
 
 
 

10. For 10 observations on Price ($X$) and Supply ($Y$), the following data obtained: $\Sigma X = 130, \Sigma Y=220, \Sigma X^2 = 2288, \Sigma Y^2=5506, $\Sigma XY=3467$. Estimate the value of the supply if the price is 16?

 
 
 
 

11. The regression equations of two variables $X$ and $Y$ are given $3X+2Y-26=0$ and $6X+Y-31=0$. What is the value of the correlation coefficient?

 
 
 
 

12. The angle between the two regression lines depends upon

 
 
 
 

13. Given the following data $\Sigma Y=294$, $\Sigma X = 490$, $\Sigma XY=3125$, $\Sigma X^2 = 5350$, $\Sigma Y^2 = 1964$ and $n=49$, then what is the value of correlation coefficient?

 
 
 
 

14. The given data $\overline{x} = 36$, $\overline{y}=85$, $\sigma=8$, $\sigma_x=11$, $r=0.6$ then find the value of $X$ if $Y=75$.

 
 
 
 

15. The slope of the regression line of $Y$ on $X$ is equal to

 
 
 
 

16. Given that $b_{yx}=1.36$ and $b_{xy}=0.613$ then the coefficient of determination is

 
 
 
 

17. The average price of an item is Rs. 25.5 with a standard deviation of Rs. 2.4 and the average demand of that item is 40 units per day with a standard deviation of 6 units. Correlation between them is $-0.8$. When the price is Rs. 24, then the estimated demand of that item is?

 
 
 
 

18. The correlation coefficient is a

 
 
 
 

19. The correlation coefficient between two variables $X$ and $Y$ is 0.8, and their covariance is 20. Also standard deviation of $X$ is 4; what is the standard deviation of $Y$?

 
 
 
 

20. The two regression equations are given as: $3X+2Y=26$ and $6X+Y=31$. What are the mean values of $X$ and $Y$?

 
 
 
 


Online Regression Correlation MCQs with Answers

  • For the two variables, the regression of $Y$ on $X$ is $4X-5Y-90=0$ and the regression equation of $X$ on $Y$ is $X+kY-6=0$. If the coefficient of determination is 0.48, then the value of $k$ is
  • The two regression equations are given as: $3X+2Y=26$ and $6X+Y=31$. What are the mean values of $X$ and $Y$?
  • Two given regression equations are $2X+3Y=5$ and $x+2Y=4$, then equation of the $Y$ on $X$ is
  • The average price of an item is Rs. 25.5 with a standard deviation of Rs. 2.4 and the average demand of that item is 40 units per day with a standard deviation of 6 units. Correlation between them is $-0.8$. When the price is Rs. 24, then the estimated demand of that item is?
  • Given the following data $\Sigma Y=294$, $\Sigma X = 490$, $\Sigma XY=3125$, $\Sigma X^2 = 5350$, $\Sigma Y^2 = 1964$ and $n=49$, then what is the value of correlation coefficient?
  • The correlation coefficient between two variables $X$ and $Y$ is 0.8, and their covariance is 20. Also standard deviation of $X$ is 4; what is the standard deviation of $Y$?
  • The covariance between variables $X$ and $Y$ of five items is 6, and their standard deviations are 2.45 and 2.6, respectively. What is the value of $r$?
  • Given that $r=0.8$, $\Sigma XY = 60$, $\delta_Y = 2.5$, $\Sigma X^2=90$, where $X$ and $Y$ are the deviations from their respective means, then the value of $n$ is
  • If $r=0.6$, then the coefficient of non-determination is
  • The statement “two regression lines always intersect at the mean value of $X$ and $Y$” is
  • The value of $b_{yx}$ in the regression equation $2X + 3Y +50 =0$ is
  • The value of $a_{xy}$ in the regression equation $2X+3Y+50=0$ is
  • The regression coefficients are equal to zero if $r$ is equal to
  • The angle between the two regression lines depends upon
  • The slope of the regression line of $Y$ on $X$ is equal to
  • Given that $b_{yx}=1.36$ and $b_{xy}=0.613$ then the coefficient of determination is
  • The regression equations of two variables $X$ and $Y$ are given $3X+2Y-26=0$ and $6X+Y-31=0$. What is the value of the correlation coefficient?
  • The given data $\overline{x} = 36$, $\overline{y}=85$, $\sigma=8$, $\sigma_x=11$, $r=0.6$ then find the value of $X$ if $Y=75$.
  • For 10 observations on Price ($X$) and Supply ($Y$), the following data obtained: $\Sigma X = 130, \Sigma Y=220, \Sigma X^2 = 2288, \Sigma Y^2=5506, $\Sigma XY=3467$. Estimate the value of the supply if the price is 16?
  • The correlation coefficient is a

Generic Functions in R

Correlation Regression Quiz 13

This Correlation Regression Quiz features essential MCQs on regression lines, coefficients, and interpretation. Prepare for your statistics exam or data analyst job test with this comprehensive correlation and regression quiz. Includes 20 MCQs on the coefficient of determination $(r^2$), regression coefficients, scatter plots, and the method introduced by Francis Galton. Ideal for students and aspiring data scientists. Let us start with the Online Correlation Regression Quiz now.

Online Correlation Regression Quiz with Answers
Please go to Correlation Regression Quiz 13 to view the test

Online Correlation Regression Quiz 13 with Answers

  • What is the necessary condition for the value of the regression coefficients?
  • Which of the following is the G.M. of two regression coefficients?
  • If $r$ is negative, then which of the following is true?
  • If the coefficient of correlation between two variables is 0.7, then the percentage of the variation uncounted for is
  • If the coefficient of correlation between two variables is $-0.9$, then the coefficient of determination is
  • The regression coefficients remain unchanged due to
  • If the value of $r=0$, then which of the following must be true?
  • What is the type of correlation between temperature and sales of cold drinks in summer?
  • The correlation coefficient shows the
  • If the change of one variable and the change of the other variable are constant (equal change), then the correlation is
  • The values of the coefficient of determination always lie in
  • The regression line, also known as
  • A numerical measure which shows a possible change in the value of $X$ for a unit in $Y$ is denoted as
  • In the regression line $Y=a + bX$, the value of $a$ is known as
  • What is the value of $b$ known as, in $Y=a+bX$ is
  • If the slopes of two regression lines are equal, then
  • What is the intersection point (common point) of two regression lines?
  • For a perfect strong correlation, if $b_{yx}=-0.5$, then what is the value of$b_{xy}$?
  • The term “regression was initially introduced by
  • If the regression equation of $Y$ on $X$ is $9X+nY+8=0$ and the equation of $X$ on $Y$ is $2X+Y-m=0$ and the mean of $X$ and $Y$ is $-1$ and $4$, respectively, then the values of $m$ and $n$ are

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