Year 2020 2021 2022 2023 2024 2025 2026 METUBE Video Views...

Year 2020 2021 2022 2023 2024 2025 2026 METUBE Video Views (billions) 0 0.3 1.5 2.6 3.4 4.3 5.0 1. Obtain a linear regression model and the correlation coefficient $r$. (Take $t$ to be time in years since 2020.) According to the model, at what rate is MeTube viewership increasing in this country? 2. Use a spreadsheet or other technology to graph the data together with the best-fit line. Does the graph suggest a quadratic model (parabola)? 3. Test your impression in the preceding exercise by using technology to fit a quadratic function and graphing the resulting curve together with the data. Does the graph suggest that the quadratic model is appropriate? 4. Perform a regression analysis using the quadratic model, and find the associated $p$-value. What does it tell you about the appropriateness of a quadratic model?

Transcript

00:01 Let's talk about scatter plots for this problem here and we'll kind of work through a and b and learn about our correlation coefficient.

00:10 Starting with a, it says describing your own way to expect the data points on a scatter plot to be distributed if the following features were present.

00:17 Okay, so we're going to start first just with a potential outlier.

00:21 All right, and just kind of visual of what would be happening.

00:25 Let's see.

00:27 All right, so we're going to have our points kind of forming here.

00:33 Then a positive outlier would be above our line.

00:37 So we have this line that's being formed from our dots, and we have this outlier, this positive outlier that's above the line, well then we would expect a slight shift up of our linear regression line.

00:51 So we'd have a shift up of our line.

00:59 We'll put line of regression to be a little bit more specific.

01:03 Okay, let's go on to our next part here.

01:08 So our next part says a negative correlation between the x and the y variables.

01:13 A negative correlation, what that means is that as the x increases, the y would be decreasing.

01:20 So as i go to the right, my dots would be going down.

01:24 So i'd have a line going down.

01:27 It's a really bad line.

01:28 So a negative correlation would result, and we could say a line of regression, and we could just put with a negative slope.

01:44 All right, and then we got one more part here.

01:47 A correlation coefficient of ours equal to 0 .9.

01:52 So now we really get into our definition of what a correlation coefficient is.

01:56 So a correlation coefficient is in between the numbers negative 1 and 1.

02:02 And the closer you are to 1 on either side, the straighter the line will be or the dots will be.

02:10 So we have a straighter we'll say compression of dots all right so having 0 .9 a positive all right our line would be going up but these dots are going to be really close together all right almost forming a straight line just kind of by themselves and then as i could not all right there would be my line okay so we could say a small dispersion all right of plots of dots all right now let's move on to part b and so part b here let's let's kind of erase our work and we'll make a new graph to kind of help us out all right so we're investigating the relationship between the time taking to upload a file and the proximity to cut up deadline okay we have 20 students who did traditionally submit their etmas within the final hour all right let's let's just find kind of the info that we really want all right so we have that that the time of submission is on the horizontal axis.

03:26 All right, so i'm gonna write that down...

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