Default is the parametric correlation, based on the bivariate normal distribution: (the Pearson correlation).Figure 73.1 includes some information concerning model fit.Some times all we want is to evaluate if there is an association between two variables or not. We specify the option SQUARE to get a square plot and want to compare the observed \(\epsilon\)’s to a normal distribution with mean and variance estimated from the data (could also write MU=0 SIGMA=1). PROBPLOT / HEIGHT=3 SQUARE NORMAL(MU=EST SIGMA=EST L=2 COLOR=RED) This is because P-P plots check if probabilities match (both axes run from zero to one) and Q-Q plots check if observations match and for this reason are more sensitive to outliers PROC UNIVARIATE NORMAL DATA=WORK.ch The special case we are interested in is the Normal probability plot, a Q–Q plot against the standard normal distribution. Q–Q plot, “Quantile-Quantile” plot, which is more commonly used.P–P plot, “Probability-Probability” or “Percent-Percent” plot.When people say ‘probability plot’ they usually mean one of two things We can also plot histograms and normal density curves using PROC UNIVARIATE PROC UNIVARIATE NORMAL DATA=WORK.ch Īnd a further evaluation of the distributional assumption can be obtained using a probability plot (also in PROC UNIVARIATE).Ī probability plot is a graphical technique for comparing two data sets, here: one empirical set (the \(\epsilon\)’s) against a theoretical set (What the \(\epsilon\)’s would be if they were normally distributed). The DENSITY is what generates the normal curve. We see that the normal distribution is not a perfect description of the observed distribution and notice how the use of options in PROC SGPLOT can change the way the plot looks. XAXIS VALUEATTRS=(SIZE=14) LABELATTRS=(SIZE=14) REFLINE -2 0 2 / LINEATTRS=(THICKNESS=2) AXIS=x HISTOGRAM stand / FILLATTRS=(COLOR=orange) ĭENSITY stand / LINEATTRS=(THICKNESS=4 COLOR=green PATTERN=3) We now evaluate the assumption that the residuals follow a normal distribution PROC SGPLOT DATA=WORK.ch LOESS y=stand X=forv / LINEATTRS=(THICKNESS=2 COLOR=red) The plot of residuals against predicted values can be created using PROC SGPLOT DATA=WORK.ch The variable stand got its label when it was created by PROC REG. Note that in the YAXIS statement we do not specify LABEL=. YAXIS VALUEATTRS=(SIZE=14) LABELATTRS=(SIZE=14) XAXIS LABEL='Obesity score' VALUEATTRS=(SIZE=14) LABELATTRS=(SIZE=14) REFLINE -2 0 2 / LINEATTRS=(THICKNESS=2) LOESS y=stand X=obese / LINEATTRS=(THICKNESS=2 COLOR=red) A plot of residuals against predicted valuesĪ plot of residuals against obesity scores can be generated using PROC SGPLOT DATA=WORK.ch.A plot of residuals against obesity scores.Generates a new data set WORK.ch with new variables forv, resid, and stand which we may then to construct residual plots OUTPUT OUT=WORK.ch P=forv R=resid STUDENT=stand We can use PROC REG to calculate and save residuals and predicted values for later use, typically graphics. Residuals where current observation is not used in estimation of corresponding line.We make this into a statistical model by including an error term that describes random variation (because it is unrealistic that everyone with the same obesity score would have exactly the same blood pressure) \[ ![]() The parameter of interest is the slope of the line \(\beta_1\): the regression coefficient: Expected difference in blood pressure for two individuals with a difference of 1 unit in obesity score. The intercept \(\beta_0\) is the intersection with vertical axis, i.e. the expected value of \(y\) at \(x=0\): The expected blood pressure for an individual with obesity score 0. So we assume that the obesity score has an effect on the bood pressure. Response variable bp and covariate obese.Linear regression is now used to study the association: XAXIS and YAXIS: larger labels, include grid.YAXIS LABEL='Blood pressure' VALUEATTRS=(SIZE=14) LABELATTRS=(SIZE=14) GRID XAXIS LABEL='Obesity score' VALUEATTRS=(SIZE=14) LABELATTRS=(SIZE=14) GRID SCATTER Y=bp X=obese / MARKERATTRS=(SIZE=12 COLOR=GREEN SYMBOL=SQUARE) Scatter plots can be created using PROC SGPLOT LIBNAME dat 'p:\sas' Īn improved scatter plot can be made by adding options in PROC SGPLOT LIBNAME dat 'p:\sas' ![]() (where OBS=7 tells SAS to only print the first seven lines in the data set). We use PROC PRINT to look at the data set LIBNAME dat 'p:\sas' We will discuss simple linear regression in this part of the course and multiple linear regression later.
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