The table below shows the number of people living in a house...

The table below shows the number of people living in a house and the weight of their trash at the curb just before trash pickup. People (x) | Trash in Pounds (y) 2 | 21 4 | 38 6 | 75 2 | 23 7 | 85 5 | 43 3 | 33 4 | 42 3 | 27 (a) Perform a linear regression on this dataset, and find the regression line. Write the equation of the line in Blank 1. Write the complete equation, starting with "y=" and do not include any spaces in your equation. Round all numbers in your equation to three decimal places if necessary. (b) Find the correlation coefficient for this data set. Write your answer in Blank 2. Round your answer to three decimal places if necessary. (c) Are these two variables strongly or weakly associated? Answer STRONG or WEAK in Blank 3.

Transcript

00:01 Okay, so i see that you need help with this problem and so it wants you to perform a linear regression on the data set and find the regression line write the equation of the line in blank one write the complete equation starting with y equals do not include any spaces in your equation round all numbers of the equation to three decimal places if necessary so to compute the equation of my line the first thing that you're going to have to do is you have to find your mean of your x then you're going to calculate your mean of your y then you're going to take each one of these x values and find the difference of it from your oh i did some and not mean average sounds like that does not look correct okay, then you're gonna take each one of these x values and find the difference between them and your mean and if we got to center these and so i'm just gonna and i understand that i'm using excel but i'm using it strictly as a calculator and to organize my data if you do not have excel you can use a paper or pencil graph paper scientific calculator even it's just going to take you a little bit longer if you do have excel you can follow along and see how i get the answers that i'm getting all right, and so then you're gonna calculate you the difference between each one of your y values and your mean of y so you're gonna take this and then subtract? your mean of 43 and then i'm gonna drag this down then you are gonna multiply this times this and then this times this and then this times this so equals this times this drag it down and then you're going to find the sum of that and that's the sum of the products then you're going to square each one of these values so you're gonna take this and square it and then you're going to do that to each one of those values and then you're gonna find the sum of that and that's called the sum of the squares of x so now to get your regression equation you're first gonna calculate your slope and to get your slope you're gonna take your sum of your products and you're gonna divide it by the sum of the squares of x so that is your sum of your products and you're gonna divide it by the sum of the squares of x.

02:40 Okay, and so bold and then to get your y intercept you're going to take your mean of y and you are going to subtract your slope times your mean of x and that is going to look like your mean of y and you're gonna subtract your slope times your mean of x and bold highlight, okay, and so your linear regression equation is going to be y equals 12 .5 x plus or minus 7 and that is your linear regression equation okay, then it says find the correlation coefficient for this data set to find the correlation coefficient what you have to do is you have to take your sum of your products and divide it by the square root of the sum of the squares of x times the sum of the squares of y so let me just merge in bold and highlight that so what that's gonna look like is your sum of your products divided by the square root square root of the sum of the squares of x whoo times and we do not calculate the sum of the squares of y.

04:52 It's gonna end up going right there.

04:53 So what you're gonna have to do is calculate that so you're going to take and this is gonna be y minus the mean of y and that's gonna be squared and i'm going to take that center and highlight bold highlight...

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