Find the equation of the regression line for the data. Then...

Find the equation of the regression line for the data. Then use the regression equation to predict the value of y for each of the x-values. Square Footage and Home Sale Price The square footages and sale prices (in thousands of dollars) of seven homes in Akron, Ohio. ?x = 11187 , ?y = 1102.6, ?xy = 2101819, ?x² = 20711509 m = 0.120 Round to 3 decimal places. b = 0 Round to 3 decimal places. y^ = 0 x - 0 Round to 3 decimal places. Multiply parts (a) - (c) by 1000 to get the answer. (a) x = 1450 square feet y^ = $ 0 (b) x = 2175 square feet y^ = $ 0 (c) x = 890 square feet y^ = $ 0 Check

Transcript

00:01 Hey there, welcome to numerade.

00:02 We are looking at the relationship between the square footage and home sale price in ohio.

00:10 So great job on finding the slope.

00:13 We are asked to find b, the intercept value.

00:17 So our slope here is equals to negative 0 .120.

00:26 Sorry, positive 0 .120.

00:34 All right.

00:37 And what we're going to do actually is write this in black.

00:52 So therefore, let's highlight this all and make it in black here.

01:03 So now with this, we are asked to find the intercept value.

01:10 Okay, so let's find the intercept value here, which is basically the b coefficient.

01:17 So our b coefficient is basically the y mean.

01:24 So we can actually combine the values here, where we have the sum of y minus the slope times the sum of x divided by the sample size.

01:47 So we can plug in the values.

01:49 The sum of y, we have 1 ,000, 1 ,000, 1 ,000, 102 .6 minus the slope.

02:00 So what we get for the slope here is the 0 .120 multiplied by the sum of x, which is around 1 ,187.

02:14 And then with this, it's gonna be divided by the sample size 7, given us a intercept value that equals around so an intercept value, that equals around negative 34 .11.

02:47 Negative 34 .11.

02:52 And we're going to actually expand it out with one more digit, 114.

03:00 So we have negative 34 .114 as our slope, 40 .120, and our intercept, negative 34 .114.

03:13 Making our overall regression equation here, y predictor of x equals our slope 0 .120 times x minus 34 .114.

03:30 All right.

03:35 Okay.

03:37 So let's carry on over here.

03:40 We are going to use this equation to plug in our square feet to predict the home sale price.

03:46 So let's start with part a.

03:49 So for part a over here, we're going to plug in to our equation, y predictor, of 1 ,450 square feet, equaling 0 .120 times 1 ,450 minus the 34 .114 for our intercept.

04:11 So with this, so with this here, we have our values.

04:23 Given us a y predictor of around.

04:29 So let's see what we get here.

04:33 1 ,450.

04:35 So we get 139.

04:39 We're going to multiply parts ac by 1 ,000 to get the answer.

04:43 So we're looking for in dollars.

04:49 So multiply parts by 1 ,000 to get the answer...