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The following dala was taken from experiment The data can be modeled by the following equation y" b * 10va6+2+0.5)0.100.300.450.550.700.440500.600.650.87Find t...

Question

The following dala was taken from experiment The data can be modeled by the following equation y" b * 10va6+2+0.5)0.100.300.450.550.700.440500.600.650.87Find the values of a and b using least square regression. Then use the resulting model to predict y at x = 0.35

The following dala was taken from experiment The data can be modeled by the following equation y" b * 10va6+2+0.5) 0.10 0.30 0.45 0.55 0.70 0.44 050 0.60 0.65 0.87 Find the values of a and b using least square regression. Then use the resulting model to predict y at x = 0.35



Answers

Use a calculator to find a regression model for the given data. Graph the scatterplot and regression model on the calculator. Use the regression model to make the indicated predictions. Find an exponential regression model for the given data:
$$\begin{array}{c|r|r|r|r|r}x & 0 & 10 & 20 & 30 & 40 \\\hline y & 350 & 570 & 929 & 1513 & 2464\end{array}$$

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.

Now, given both of these regression models, one of which is a multi variable having two independent variables X. One and X two And the other one, X 2 is discarded. And we simply use X one tomato. A certain phenomenon With a regression model. Now we may notice that the values for X one are different in each of these cases. When X two is present, it's 8.63 And when X two is removed We have 9.1. Now the interpretation behind this difference, it's simply that for the case that there is a single variable in the regression model, the coefficient of the independent variable gives us an estimate of the change and why or the control variable given a one unit change in the independent variable X one. For example, if we increase the value of X by one, we can expect the estimate of why to go up By 9.01. Very well now, what about the multi variable case? The coefficient of X one represents an estimate of the change and why For a unitary change in X. one when all of the other variables are held constant. Now noticing the differences between the coefficients in each case is what can be attributed to this difference. Now, multiple in Merete is the occurrence of inter correlations among two or more independent variables in a regression models such as this. So multi culinary T can lead to misleading results when attempting to determine the influence of individual variables, and for that reason it's better to employ variables that are independent from each other. They are not correlated or dependable in any way.


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