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Question 5 (3 points)Evaluate the regression coefficient (the statistic you computed) from the first question above_ Interpret it as discussed in class (You should ...

Question

Question 5 (3 points)Evaluate the regression coefficient (the statistic you computed) from the first question above_ Interpret it as discussed in class (You should be able to answer this in one sentence:)

Question 5 (3 points) Evaluate the regression coefficient (the statistic you computed) from the first question above_ Interpret it as discussed in class (You should be able to answer this in one sentence:)



Answers

Using the regression out- put in Exercise 1, identify the standard deviation of the residuals and explain what it means in the context of the problem.

Here we are asked to look at the output from exercise to and to identify and explain the standard deviation of the residuals in software output. The standard deviation of residuals is usually given as yes or s of E. And in this case, it's s So we have the residual standard deviation is equal to 5.13 So remember that the residual standard deviation gives us an idea about how far the sampled points typically spread vertically from the modelled regression line. And since the white accesses goals, the units of our residual standard deviation is also goals. And since our data per seen pertains to generally less than about 50 goals, a residual standard deviation of 5.13 tells us that her model can give moderately high errors relative to what we're trying to estimate.

Once again welcome to a new problem. Uh, this time we're still dealing with regression analysis. And one of the things that happens is if it's ah, by variant, by a variant regression, it simply means that you have ah dependent independent variable, which is typically the X. And you also have, ah, dependent variable, which, in this instance, is the is the why but a multi varied regression, Multivariate regression or what we sometimes call multiple regression. This is where you have multiple independent variables like X one x two and then you have a dependent variable, Which is why so x one and X two could be something like income and education. And those have an impact on the dependent variable. Which is why so in this particular problem, we are given, uh, regression equation assumes that why heart is our regression equation. And it's the same as 29 point, um, 1270 on and the 29.1270 that represents the, uh, intercept. Obviously. And then, of course, we're gonna have the slope, you know, 0.590 six x one and then also have point 4980 Uh huh. X two. So what you're seeing right now is a regression equation which has an intercept. This is our intercept. And then there two independent variables that you're looking at X one and X two. So the first part of the problem in but hey, we want to figure out the meaning off the two slopes, which we're calling B one and B two. You know, what's the the meaning off these slopes and then in. But we want to figure out the value of why given that's the independent. Variable X one is the same. 180 on the second independent variable is the same was 310. So that's what we're given in the problem. So in part a was saying, if y heart is the same as 29.12 70 plus 0.5906 x one and 0.4980 x two these two values that you're seeing right here. This is the initial slope B one and this is the second slope be too. And by slope, we mean the changing. Why relative to the changing eggs we're using why heart? Because this is the predicted value and X is the predictor. So if you complete specific number of years of school, which is education, for example, you're supposed to have a certain amount of incomes or were predicting that the reason why we're using why heart? Because this is a sample prediction to sample prediction. The equation models example. So why is theme the actual population value as opposed to why heart, which is a sample value so want to interpret the meaning off slopes that slope is the relative changing the predicted values or the slope is the relative change, uh, in predicted. So values, um, given specific predictor values. So in this case, I'll predictive value is Delta X human. You change by one unit. So ah, unit change in X produces, uh, be change and why? That's the interpretation off your slope. So be one is the same as 0.5906 Meaning that, um, increasing x one by a single unit increases Mhm. Why buy 0.5906 And then, of course, the second one that we're seeing, Um, And in the first instance, assume x two is constant. And this happens on then the two is, um, zero point 4980 which means that you're increasing likes to buy one unit mm. As why this is so a y increases it quizzes by 0.4980 units. So that's what's happening in this particular problem. And we get to see get to see that If you're increasing the units like that, that's what's gonna happen. And that's B one and B two. In this particular problem, the meaning and interpretation assume X one is a constant whenever you're changing and x two so x one remains a constant. In the second instance, we have two instances there. That's what a on then, of course, you know we're going to jump onto Part B and the requirement for parties that we wanna make predictions. We know that Ah White Hart is the same as 29 point oh 1270 plus 0.5906 x one plus 0.4980 x two Gonna plug in specific numbers into the equation. So we have 0.5906 Of course, we'll plug in X one and X one was given us 100 80. That's our plug in. And then, of course, we have a 0.4980 of a second plug in in this case is 310. That's our X two. If you simplify that problem, the result it's gonna end up being. So we're going through the multiplication process. We have 291270 plus 100 and 6.308 154.38 And our final prediction or final final answer becomes 289.815 That's our predicted value. That's all predicted value. So once again we had a problem and the problem had two sections. The first section is we were supposed to interpret the meaning off these two slopes what we're calling be one and B two. So that's the first part of the problem. The slopes reflect changes in the Y value the predicted value, with each one of these staying as a constant as the other ex independent value changes. So we found the slope with Far Slope is 0.5908 2nd one is our 0.4980 and then we plugged in 180 returning to x one and x two and predicted all value to be to 18. 89.815 So I hope you enjoy the problem. Feel free to send any questions or comments and have a wonderful day.

All right. So they gave us a data set. The first thing they want us to do is create a scatter plot. I'm using Dez most. It's an online graphing tool. And so when you open up dez most dot com, you can go over here and click the plus sign, and we're gonna enter a table of values. So I'm gonna go through an inter mo table. You're my exes, and then I'm gonna enter my wives ground. When you look at your chart, you can move your graph around so that you can see it. This looks like it could be an exponential curve. It looks like it's starting up and coming down, but it's staying inside this positive. Why access thing? So we're gonna try Exponential, you're exponential general form. Okay, It's gonna be why one and then we want to use the tilde for their aggression. Let's try a B to the X of one. Oh, my goodness. I don't think we could get any prettier going through those notice. How close are squared is toe one. And if we plotted our residuals there almost sitting on ze road, which is amazing, it's a great, great regression there. So to write that equation, we would have y equals R A value 3.141 times are be value 0.8 of eight. And we're gonna raise that to the X. Make sure you put your be in parentheses or you won't get that same look. But there is our regression equation for this data set.

All right, so in this question, they give us a data set. They want us to create a scatter plot. So I'm using Dez most. It's an online calculator. And so what I did here was I entered a table or I did enter a table here. I entered a table of values you can see here that I put in the X and the Y from question 12 and put those data points in, and they have grabbed them. You can drag a graph so that you can see them. Or if you need to resize, you can use the wrench to resize the X and y axis appropriately. Now, when I look at that, I'm trying to determine which regression to use. Well, this kind of looks like it could be a power, or it could be a quadratic, and so we can shot different things. I'm gonna try quadratic because it kind of looks like it's got this this u shaped curve that goes up It's just like a real flat quadratic sort of. And so if I go and try that, gonna use my standard form with my till that that's my regression up in the top left usually. And so we're gonna do a X one square plus B x one plus c. I noticed that when you do that, you get your your statistics here. Notice that your R squared is very close to one, which is good. If we were to plot our residuals, they're really close toe one. That's good. So this is a pretty good approximation of this curve. And And if we wanted to write that equation with the re vestibule places, we would have negative point 055 x squared plus 1.656 minus 7.715 And you can see how Brad is the right equation. It does match up to my data. So there's your regression equation. Why'd radically in that problem?


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