ED 793 LAB # 5LAB #5 OUTLINE Correlations with p-value: Testing the significance of the relationship between two variables. Simple Linear Regression: Determining how well a model fits the data and how well the independent variable in the model predicts the dependent variable.Correlation CoefficientAlways use scatterplots to visually examine the relationships between variables. Note that the syntax below is plot y with x. PLOT /PLOT SATM WITH HSGPA. Test of a Correlation Coefficient*Hypothesis testing for correlations, two-tailed.CORRELATIONS VAR=HSGPA COLLGPA /MISSING=LISTWISE.Correlation Output:- - Correlation Coefficients - - SATM HSGPA SATM 1.0000 .4955 ( 2601) ( 2586) P= . P= .000HSGPA .4955 1.0000 ( 2586) ( 2586) P= .000 P= .  Correlation Coefficient for HSPGA and SATM 2-tailed significanceSIMPLE LINEAR REGRESSIONThings to know/keep in mind about linear regression:1. Regression analysis explores how independent variables explain the variation of a dependent variable1/15/19 ED 793 Lab12. Linear refers to “linear in parameters” not variables. 3. There are several different methods of estimating coefficients. The most common method is OLS (Ordinary Least Squares) regression, which we’ll use today and for your projects.4. There are several different ways for adding the independent variables into the regression equation. Today we are using what SPSS calls “enter” which means user specified. 5. Generally, you get two coefficients listed on the output, we will focus on the unstandardized coefficient for now: The unstandardized coefficient, B: based on the unit of measure that the independent variable comes in. It is used for discussing the effect that variable has on the dependent variable. The standardized coefficient,  (Beta): is a standardized version of B. It is used for comparing the strengths of the effects of different independent variables.6. When judging your model and how well it explains the variance in the dependent variable, you want your R-squared (R2) to be close to 1. If R2 = 1, the model is perfect (explains all of the variance). In educational research, it is not uncommon to see values as low as 0.15 or 0.20.An exampleLet’s say we wanted to see how well we could predict a student’s score on the SATM. We might theorizethat the student’s high school gpa (HSGPA) is a possible predictor. My independent variable is SATM, and independent variable is HSGPA. The regression model looks like this:SATMi = 0 + 1 * HSGPA + ei THE COMMANDSREGRESSION /VARIABLES=SATM HSGPA /DESCRIPTIVES=MEAN STDDEV CORR /DEPENDENT=SATM /METHOD=ENTER.REGRESSION tells SPSS you want to perform a regression analysis./VARIABLES=list of variables identifies for SPSS the variables in your analysis./DESCRIPTIVES= MEAN STDDEV CORR tells SPSS to put the mean, standard deviation, and correlations for the variables in your output./DEPENDENT=variable name identifies for SPSS which of the variables in the /VARIABLES= line is yourdependent variable./METHOD=ENTER is a command that tells SPSS to enter the variables as they appear in the syntax. 1/15/19 ED 793 Lab2THE OUTPUT * * * * M U L T I P L E R E G R E S S I O N * * * *Listwise Deletion of Missing Data Mean Std Dev LabelSATM 551.894 113.183 SAT MATH SCOREHSGPA 5.964 1.601 AVERAGE HIGH SCHOOL GRADE N of Cases = 2586 Descriptive Statistics are printed on Page 7Block Number 1. Method: EnterVariable(s) Entered on Step Number 1.. HSGPA AVERAGE HIGH SCHOOL GRADE Multiple R .49551R Square .24553Adjusted R Square .24524Standard Error 98.33016Analysis of Variance DF Sum of Squares Mean SquareRegression 1 8130609.69031 8130609.69031Residual 2584 24984230.06568 9668.81968F = 840.91026 Signif F = .0000------------------ Variables in the Equation ------------------Variable B SE B Beta T Sig T HSGPA 35.027732 1.207917 .495507 28.998 .0000(Constant) 342.973420 7.459502 45.978 .0000A KEY TO THE OUTPUTR square An estimate of how much variance in the dependent variable is explained by theindependent variable(s). Adjusted R square It is the R2 value, mathematically ‘adjusted’ for the number of predictors in the model. It is a good idea to report your adjusted R squared. 1/15/19 ED 793 Lab3Multiple R This number is squared to get R square. It is the correlation between the dependent variable and the set of predictors together. In our case, with one predictor, this value should equal the raw correlation coefficient computed earlier. F It tests H0: 2 = 3 = 4 = … = k = 0 or H0: R2 = 0. We call this a goodness of fit test. Do the independent variables explain a statistically significant amount of the variance in the outcome? B This column gives you the estimated unstandardized coefficients (raw units).SE B This is the standard error of the estimated coefficient (B).Beta This column gives you the standardized coefficients (standard deviation units).Sig T The probability that we would see such a t-value (see above) if the real linear relationship between the variable and the dependent variable was nonexistent (nullhypothesis true).INTERPRETING THE OUTPUTThe regression output consists of three blocks of information. The first block we see is a listing of the descriptive statistics and the correlation matrix that we asked for. The second block has the “Goodness of Fit” measures. The last block is about the statistics for the independent variables in the model. See the output above for the matching symbols (e.g., ) that go with the discussion below.Listwise deletion of missing data. This means that only cases which have values for all variables are included in the analysis. This means that hsgpa accounts for about 24% of the variance in satm, That’s pretty good, though it tells us that there is plenty of variation in SATM scores that hsgpa does not explain.  The F-statistic is the global model test. (F=840.91026 Signif F =.0000) These are the estimated coefficients—that is, the amount that SATM will change for every one-unit change is the independent variable holding all