The following estimated questions used the data in L A M L L MLB High, which contains information a major league baseball salaries. So the dependent variable s salary is the log of the salary and it's two explanatory variables. I s in the major leagues. I'm giving the equations. So the first question says, how many degrees or freedoms are in intra aggression and outcome there. CR is smaller in the second regression than in the first. So we're going to consider did some models first, which is which I'll be writing. Yes. And there's you create the other model is this'll Yeah, Klaus on this under here is so these are the two models on the formula to find the degree of freedom is showed as d f you think cost to end minus K plus one. So, yeah, the end is the sample size on the came first one is the number of estimated parameters. So the degree of freedom for the first regression would be D f because t o n minus K minus one and opened this and this is going to be called to 353 minus one, minus one. And is he called 35 phone. Now the degree of freedom for the second drink regression. So this is the first The second regression We d f equals toe end minus K minus one. This is the cause of 353 minus two minus one on this. Because the 3. 50 now in the second requestioning question the number of explanatory variables, um gets increased on. As a result, the SSR is increased on the S e l on s S s s are positively related. So s S R increases on S c r on S S r positivity related. Now the SCR decreases due to reducing beauty, reducing the value of the SSR. So this is the reason why this simple linear regression of smaller SCR values So the s e r decreases due to reduced value off the SSR. So that's what we can tell now moving on to the next question. The example Coalition coefficients between the years on r B. I S Y is about 0.487 Does this make sense? What is the various inflation factor for the slope coefficients in the multiple regression? Would you say there's lead to moderation or strong culinary ity between the years on the r B I s Y are so for this to crush coalition coefficient, the coalition represents the information. So for values between 1.0 on 0.5, they have strong linear relationship for bodies between 0.3 um 0.5. They have moderate post it Steve Linear relationship Now for values between their points, one on 0.3 have weak, positive linear relationship. Now for values that was their points would have no or very weak linear relationship. So the correlation between the years correlation between yes on and that is 0.487 on it's considered the correlation is moderately. Since it's this, it's moderately positive is going to be on this. So is moderately positive in nature because it's close to 0.5. So therefore it makes sense, right, And now the various inflation factor can be calculated. US. V. I f is the cost to one divided by one minus R squared. Yes, on R squared yes is equal to 0.5 597 So put values of our square years in a formula and you get one divided by one minus 0.597 on this, because toe one divided by 0.403 So the f is two point for 814 So therefore, this is the V F on. This represents the value below the value. One is that values. Remember that valley one. What you want is values. The are not coral. It said valleys between one on four. Our values that moderately correlated values that greater than four. Our values the I li correlated so we can tell that 2.4814 represents value. Mr um Moderately correlated. So there's a moderates, Corrine ality between the years and the RBS I as valued lazier. So that is in moderate called narrative. Okay. Between? Yes, um, yeah, as via ev. Nice between, what? On fourth? Yeah, Now moving on. How come the standard error for the coefficient on years in the multiple regression is lower than its counterparts in the simple regression? So, in the second regression equation, do you know about explanatory variables get increased and as a result, S S R is increased on S e. R. On S S R is positively related. Now the SCR decreases due to the value off reducing value off this. So s E r. Decree this, dude. So the reducing value off S S r on This is the reason why simple in the immigration have smaller S e r values.