 Students, today we are going to study the multivariate regression analysis using SPSS and R, when we will use the multivariate regression analysis. So, we have the one independent and one dependent variable, we will use the simple linear regression. We have the one dependent and more than one independent variable, we will use the multiple linear regression. So, when we have the two and more than two dependent variable and one and more than one independent variable, then we will use the multivariate regression analysis. So, here the multivariate regression analysis using SPSS and R, we will check with both methods how we use the multivariate regression analysis. Here is the numerical example of multivariate regression analysis. Suppose, we want to predict a student's final grade in two subjects, math and science. We have to predict the student's final grade in two subjects, math and science. Based on, because this is the dependent variable, based on their study hours, how many times they study, and the extracurricular activities and their extracurricular activities, how many are there? This is the hypothetical data with 20 students. We have collected the data of 20 students and then with a multivariate regression model. Why did we use the multivariate regression model? We have used the simple regression model because here we have the two dependent variable. On the above data section, to predict students' final grade in these two subjects. What do we have to predict? Student's final grade in these two subjects based on their study hours and the extracurricular activities. Here is the data. So, we have total 20 students. This is the total 20 students. What do you have? Study hours, extracurricular activities, math's marks and the science marks. Basically, grades we have marked them. Further, now you have the types of multivariate data because there are two dependent and you have two independent variables. To perform multivariate analysis using SPSS, how will we perform it? Specify the dependent variable. First of all, you have to specify the dependent variable. Here is this example, we have the math grade and the science grade. These are the dependent variables. And the independent variable is specified. We have studied the arts and the extracurricular activities. In the first step, we have specified. Then, what do we have to do in the second part of the first step? Specify the regression equation. We are specifying the equation. These are the dependent variable, math grade plus science grade. These are the dependent variable based on their study arts and the extracurricular activities. These are the independent variable. So, what did we do first? Set up the regression model. We have set up the model. Now, the second step is the run the regression analysis. Now, how will we run the regression analysis? Run the regression analysis using the specified variables. A variable we have specified. These are the independent and these are the dependent variable. We have specified that. Then, obtain the regression coefficient, p-value, myer of, model fit, example, R-square and the adjusted R-square. Now, we have defined it. Finally, we have interpreted it in step 3. We are not doing any testing in a particular example. We are doing model fitting. Okay, student. Now, I am taking this data in SPSS. This is the data in SPSS. What did you have? Here is the student, study arts, extracurricular activities, math and science. Okay, we have shown the data in the data view. In the variable view, you have a student because he has an ID. He is also from America. Student arts, numeric, extracurricular activities, numeric, math and science. We have numeric type. If you want to open a decimal in it, you can open a decimal. But in particular, we don't have a decimal in the example. Okay, how did we perform it? Go to the Analyze, then Journal-Linion model and go to the Multivariate. Check the Analyze, Journal-Linion model and Multivariate. Okay? Then, what were the dependent variables? You have dependent variable, Maths and Science. We have that in the dependent variable. Independent variable, study arts and extracurricular activities. Where did I take this? In the covariates. You have checked that in the dependent variable, we have entered the dependent variable Maths and Science. And the independent variable, which we had, I have entered in the covariates. Then go to the Model. We don't have to touch the Model. Then Option. Which one do you have in Option? We have to estimate the Parameter. Okay? Look at this. Here is the option, Parameter-Estimate. Parameter-Estimate has a significance of 0.05 and Confidence. Interval is 95%. Click Continue and the OK. Now, look at this. These are the Parameters. Estimates are here. Dependent variable, Maths and Science. Be coefficient. You have their coefficient. And t-statistics, standard error and the significance level. Significance value and their 95% Confidence. Interval is here. Now, make a model from here. What is the model for Maths? Model Y. Be coefficient. And these are the standard error. Now, what do you have in Be coefficient? Model, Intercept, 63.503 plus Steady-Arts, 4.032. Steady-Arts has been called X1. And the 0.593, you have extra colloquial activities. Multiply by X2, X2, what do we have? Extra colloquial activities. Okay, from here, we have Model-Generate for Maths. Then, for Science, we have Model-Generate. Constant, 63.650 plus 2.105 Steady-Arts, X1. And plus 2.037, Multiply by Extra Colloquial Activities. And here is the R-Square. R-Square, which is equal to 0.943. And the R-Square, this is for Maths. And this is for Science. R-Square, which is equal to 0.867. So, what do we have here? Model-Generate. And if we look at the significance level, we have Steady-Arts, which is significant for Maths. And for Extra Colloquial Activities, we have N-Significant for Maths. Similarly, Steady-Arts is significant for Science. And same as Steady-Arts, we have Extra Colloquial Activities, which is significant for Science. This is the SPSS window. Now, we will interpret our results. Here is the model. What is the model you have? Model-YM, 63.503 plus 4.0, 4.03, 2X1. Who did we call X1? We called X1, we called Steady-Arts, and X2, we called Extra Colloquial Activities. Okay, this is the model for Maths, dependent variable, and this is the model for the Science. And here is the R-Square value. Now, what do we do? We are predicting it. What did we do in prediction? If, now the students are with us, this is the Steady-Arts, and here is the Extra Colloquial Activities. Okay? X1, Steady-Arts, this is the Extra Colloquial Activities. If, this is when, or you can say that if, X1, if those two are Steady-Arts, two are Steady-Kare Sira, and participate in five activities, five Extra Colloquial Activities, then how many marks of Maths will come? The marks of Maths will come approximately 75 percent. Okay, 74.557 approximately 75 percent will take the marks of Maths. Same this is, if they study two arts, and participate in five Extra Colloquial Activities, then how many marks of Science will come? The marks of Science will come approximately 78 percent. This is the prediction. This is the regression model. We predict here basically in regression model, and we have also generated regression model. And from there, we predict that if he will study so many arts, and participate in so many Extra Colloquial Activities, then we will get the marks of Maths in 74 percent, and the marks of Science in 78 percent will come. That is, 78 percent marks will come. And how did this happen? We have generated X1, we have multiplied it by two. X1, 5. And we have taken two here. Then we have got the estimated value of the marks. This is the multivariate analysis using SPSS. Now we are doing the same thing in R. Now we are going for R. We have to fit the same model in R, multivariate model. This is the window of art studio. Okay, where do you have the data? We have the data in SPSS. Let's import the data. Here is the import from SPSS. Browse. On desktop, I have the data of SPSS. You have the data of student's study arts, Extra Colloquial Activities, Maths, and Science. We have imported it. Look at this. This is the data. Now we have the data. Here is the lecture underscore one or two. Next we have the file. Here we have the data. From where we have taken the data equals to lecture one or two. Here we have the data. After taking this data from here, next we have. Now what variables do you have in the data? In the data you have Maths, Science, Extra Colloquial Activities, and Study Arts. Here I have variable y1 equals to lecture underscore this. Now I have copied and pasted it by writing it again and again. Lecture underscore this. Here is the dollar sign. So I have the dollar sign. What is it? Here I have first Y1, Maths. Because this is the dependent variable. That is why I said Y1, Maths. So Y2 equals to lecture. Here you have second dependent variable, Science. Enter X1. This is the independent variable. X1 equals to lecture underscore this. Dollar sign. What is it? Extra Colloquial Activities. What is this? We have imported the data. We have defined the Y1, Y2 variable in the data SPSS file. Y1 is the dependent variable of Maths and Science. X1 is the independent variable of Study Arts. And the X2 is the independent variable of Extra Colloquial Activities. Then what we have to do here? Multivariate multiple regression. So MMR, let Kalyan, Multivariate multiple regression equals to LM, linear model, parenthesis, C-bind. Again, parenthesis, dependent variable we have Y1, Y2. These are the dependent variable. Tends to independent variable X1 plus X2. Model is here. This is the dependent and here is the independent variable. Now run this. Yes, model is here. After model runs, we just say further that give me summary. Summary. Summary MMR. Let me find summary of R. From here, look at MMR. This will also run with us. Now look at this. This is the model. This is the C-bind, Y1, Y2. Y1, Y2. These are the dependent variable. X1, X2. These are the independent variable. The same result we have is coming in SPSS. R may be. I have told you the method of R. How we will run multivariate multiple regression in R? Intercept, you will remember, we had 63.503 there. And science's intercept, we have 63.650. Same is X1, maths, 4.032. For Y1, we have X1, maths for Y2, 2.105. For X2, we have 0.598. And for Y2, we have 2.037 for Y2 variable. The same result is coming in SPSS. And the same result is coming in R. So, this is your choice. You can do this with SPSS, with ART. There is no difference in results. Now, if we check it individually, I am running this summary. Because I have written the summary. I think I didn't run the summary. We will run the summary. Now, the summary is run. What did the summary do? First, we did response variable Y1. According to Y1, it determined all this. Then, the summary gave us Y2. Y2, response variable Y2. So, we have values of Y2 in the summary. 63, 2, 2. Same results. And Y2's response. And if I look at Y1's response. So, 63, we have intercept. 4.0 days. And the value of X2 is 0.59. Same, these are the results. And the R-square value. R-square is the 0.9, 4, 2, 6. Same result is coming in SPSS. And here you have R-square value for science. 0.8671. If we go to its testing, then what we have? Model is best fit. Because we have R-square value. High value is coming. It means we have model best fit. This is the solution of the multivariate multiple regression for R and the SPSS. We have made a model build. And the model build is telling us. Can you find it from R or from SPSS? Who? Multivariate multiple regression. When do we use multivariate multiple regression? When we have more than two dependent and more than two independent variable. Then we will use the multivariate multiple regression. Here is the conclusion of this example. The multivariate multiple regression. Using R and SPSS, we checked both. We have used multivariate multiple regression from R. And we have used multivariate multiple regression from SPSS. We have checked the results from both. The results from R and SPSS are the same. They have different methods. We have studied the methods here. After studying the methods, how do we use them? With this particular example, you have an idea of when we use multivariate multiple regression when we have two dependent and more than two dependent and more than two independent variables. So, we can easily run multivariate multiple regression. So, this is the example of the multivariate multiple regression using SPSS and R.