Speaker 1: Hi everyone. In this video, we will learn how we are going to interpret these regression results. I have already explained you in my previous video how we are going to perform regression using Excel using data analysis toolpath. And here as you can see, performance is in this analysis, performance is my dependent variable that is represented by Y and size is independent variable that is represented by X. So, that means we just want to check firm's performance and that depend on size of the firm. Size of the firm we have taken only on the basis of the number of the employees. And here is performance and size we just want to check, we want to run regression. I have already explained you all these terms what is multiple R, what is R square, what is adjusted R square and standard error and observations. Multiple R square simply it is reflecting what is the correlation in between both these variables and this is the Pearson correlation coefficient. And R square that is always reflecting means coefficient of determination, it is simply multiple R square and R square measure the proportion of the variation in your dependent variable explained by your independent variables for a linear regression. And adjusted R square it is better model. When you compare model that have a different amount of the variables, the logic behind it is that R square always increases when the number of value variable increases, meaning that even if you are, I mean that particular independent variable contribution is 0. When we talk about standard error, standard error, right, we are going to calculate a standard error means what is the difference between actual and predicted value that would be standard error. So, standard error of the regression is the average distance that the observed value fall from regression line, smaller the regression error, regression means more accurate result. Now, we come to the, we will put all these values in this equation, y dependent variable, x independent variable, y is equal to a plus bx. What is a? a means intercept and b means beta coefficient or we can talk about the slope. So, what we have got? You can see here this table. We have received this table through data analysis toolpath. Intercept is 6.86, intercept and what is the slope is 0.16. So, let me calculate y is equal to a plus bx. So, what I am doing here, simply I am just putting equal sign and what is the value of a? We can see a 6.86. I am just putting here 6.86, right. Then after that I am writing here is the plus sign and b, b is my slope, so 0.16. And what is the value of x? Let's say, I just want to, and simply you have to press x, but I want to take x value is 20. So, what I will do? It would be multiplied by, let's say 20. So, I will press enter. So, now you can see 10.06. So, let me check whether this value is same, right, when we had calculated. Yes, you can see here, this value is same, 10.07, that is same. Now, we just want to calculate right through the predicted performance when we had applied this regression analysis, this value and manually calculated value both are same. That means a model is correct. Model we can say means our process to calculate that is correct. Then we come to the residuals. Residual is basically actual minus predicted. So, what is my actual value? How we have got this? Actual value is, we will talk about, that is our actual value. Let me calculate equal to, actual value is, this is my actual value, right, and minus this is my predicted value. Let me check what is my, this is my predicted value.

Speaker 2: Enter. No, just a moment. This is my actual value and this is my predicted value.

Speaker 1: This is my predicted value. This is my predicted value. Enter. So, now you can see 0.167, that is my residual and same residual you are, you can see here, that is, residual is here. And one more thing, what is the importance of this ANOVA table? ANOVA table is very, very important. Significance F is the most important. If I have created two hypothesis, one is the null hypothesis. Null hypothesis what is said, no relationship between form's performance and size. But alternate hypothesis said, there is linear relationship between form performance and size. So, as for the model is significance because, why it is significance? Because it is less than 0.05. These values are less than 0.05. You can see here, that is reflecting here. So, in our case, we would accept all, this one is the alternate hypothesis. We are going to reject this null hypothesis. This value is more than 0.05, right. So, what we have to do? We are going to, we will write here, we have failed to reject null hypothesis and we are going to reject alternate hypothesis. Because this significance F value is greater than 0.05 or less than 0.05. That will decide your acceptance or rejection of the null and alternate hypothesis. So, I hope intercept value is clear to you. Beta value is clear. Y is equal to a plus bx. This equation is clear to you. And significance, how, what is the meaning of this significance F? That is clear. On the basis of which, how we are going to accept and reject null and alternate hypothesis. So, I am sure in the next video, I am going to discuss some more, some more interpretation points of the regression in this video. Thank you so much. Stay tuned. Keep watching.