14. A regression equation is given by y = 11.37395 +...

14. A regression equation is given by $y = 11.37395 + 2.82773x$. The following information about the variable $x$ and $y$ is also given $\sum y = 255$, $\sum y^2 = 8621$, $\sum x^2 = 480$, $n = 8$ Calculate the value of $\sum xy$. (HINT: You will need the value of $\sum x$.) A. 1552 B. 1987 C. 2017 D. 3251 15. For the data in Question 14, calculate the correlation coefficient. A. 0.992 B. 0.982 C. 0.892 D. 0.809 16. The table below shows information about points scored by 4 basket ball teams in a league season. Standard Mean number of Team Games played deviation of the points points Team 1 84 74 9 Team 2 76 93 10 Team 3 76 69 8

Transcript

00:01 In this problem, you were given the regression equation, the sum of y, the sum of y squared, the sum of x squared, and the fact that there were 8 pieces of data.

00:10 And our ultimate goal is to calculate the sum of xy, but in order to do so, we'll first have to find the sum of x.

00:20 Since our regression equation is based on averages, then i can modify that formula to say that y bar equals 11 .37395 plus 2 .82773 x bar.

00:42 And i can calculate y bar by saying y bar is equal to the sum of y divided by n, so i could say that y bar equals 255 over 8.

00:59 So i could substitute that in and say 255 divided by 8 is equal to 11 .37395 plus 2 .82773 x bar.

01:18 I could then subtract the 11 .37395 from both sides, and i will get 255 over 8 minus 11 .37395 is equal to 2 .82773 x bar.

01:50 I could then divide both sides by 2 .82773, and i will get that x bar equals, and when i calculate this all out, i will get that x bar is equal to 7 .25002652.

02:22 And then if i use the fact that x bar is the same as the sum of x divided by n, then the sum of x is equal to n times x bar.

02:38 So if i take the x bar value and multiply it by 8, i will get that the sum of x is equal to 58 .00002122.

03:04 And that's pretty close to 58, so we're going to say that the sum of x is 58.

03:10 Next we're going to go back to our regression equation, and our regression equation was y equals 11 .37395 plus 2 .82773 times x.

03:29 And we want to calculate the sum of xy.

03:34 So if i multiply both sides by an x, then i get that xy is equal to, and i can distribute, i would say 11 .37395 plus 2 .82773.

03:56 And i distributed the x, so this technically would have x here, and i'll have an x squared here.

04:09 And then if i say the sum of xy would equal 11 .37395 times the sum of x plus 2 .82773 times the sum of x squared.

04:34 So the sum of xy equals 11 .37395 times the sum of x, which we said was 58, plus 2 .82773 times the sum of x squared, which was given to us to be 480.

05:02 When you calculate that out, you are going to get our sum of xy.

05:07 And our answer choices were a, 1552, b, 1987, c, 2017, and d, 3251.

05:31 So i'm going to bring in my graphing calculator, and my graphing calculator is the texas instruments brand calculator.

05:38 And we're going to perform that math.

05:44 So we're going to do 11 .37395 times 58 plus 2 .82773 times 480.

05:57 And we are getting 2016 .9995...

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