A researcher wishes to see whether there is a relationship...

A researcher wishes to see whether there is a relationship between number of hours of study and test scores on an exam, she must select a random sample of students, determine the hours each studied, and obtain their scores on the exam. Table can be made for the data, as shown below Student | Hours of study | Score (%) --- | --- | --- FESS | 6 | 82 FCVAC | 2 | 63 PADU | 1 | 57 FBA | 5 | 88 FELS | 2 | 68 CGS | 3 | 75 a) Determine the dependent and independent variable for this study. b) Calculate the coefficient of correlation, r and interpret the result. c) Calculate the coefficient of determination, r² d) Obtain the coefficient of regression estimates of ?? and ??. d) State the estimated least square regression line. e) Interpret the y?intercept, ?? and the slope, ?? obtained in (d). f) Predict the grade for 4 hours of study in the statistics class

Transcript

00:01 All right, so we're given some data that a researcher collected because they wanted to see whether there's a relationship between the number of hours of study and the test scores on an exam.

00:13 So here's the hours of study in this column and these scores in this column.

00:20 And we want to first determine the dependent and independent variable for the study.

00:25 So the hours of study, we're going to call that our independent variables.

00:29 This is part a.

00:30 Independent is the x, the hours of study.

00:33 Is why the score because it only makes the most sense that the hours of study will will influence the score as opposed to the score influence the hours of study the score you receive influenced how much hours how many hours you studied to get that score that's not really how this is work now we're going to calculate the coefficient of correlation so i use this formula here there's a few different ways you can get this so you need the sums of the x's, some of the y's, some of the x squared, sums of the y squared, and some of the product of the xy.

01:11 So that's what these values are here.

01:14 This row here is the sum of the, right here's some of the x's, some of the y's, some of the x squared is 79, some of the y squared is 31 ,934, 35, and then the sum of the xys is here.

01:33 So there we go.

01:33 So we have those.

01:35 We substitute those into the formula here.

01:38 Just be careful with the order of operations that we get the there's a pair of parentheses underneath or within the square root in the denominator.

01:47 So just be aware that.

01:48 So we get 0 .92.

01:52 So it's b.

01:54 And the way we interpret this is that there is a strong positive correlation between the hours of study and the score of the exam.

02:03 So strong positive because it's positive.

02:06 Strong because it's close to one.

02:08 Coefficient of determination is r squared you take the r value and you squared so 0 .92 squared is 0 .8 496112 0 .79 and we interpret this as a about 85 % of the variation we see in y and the score can be explained by the variation we see in the hours of study or x now we're to calculate the coefficient of the estimates for bait it says we're given beta not in beta 1.

02:42 Beta not is our intercept.

02:43 I have that as a.

02:46 And beta 1, that's the slope.

02:49 So this is our y -inth.

02:52 Percept.

02:53 Why intercept that is? and then we have our slope right here.

03:01 That's given as b.

03:04 And we use the same sums as before to get them.

03:07 So we use the formulas.

03:08 So you can substitute those in...

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