Question

The following table provides data for a sample of nine random homes sampled that compares the square footage of the home (in hundreds) and the price of the home (in thousands) Sq ft: 35 21 41 25 27 37 32 41 26 Price: 310 298 380 307 326 461 498 524 275 a. Plot out the scatterplot of the data on the graph below. Be sure to label your axis with reasonable units and label the units on each axis (ie, which is the sq ft and which is the price) b. Does the data seem to be linearly related, and if so, is the data related in a positive or negative way? c. What is the value of the correlation coefficient? What does that say about the data? d. Calculate the regression equation e. What does the slope of the regression line represent in terms of size and the price of a homes in this area (use specific numbers here)? f. Use the regression equation to determine the price of a home in this area that has 2600 square feet. g. Use the regression equation to determine the square footage of a house that is $375,000

          The following table provides data for a sample of nine random
homes sampled that compares the square footage of the home (in
hundreds) and the price of the home (in thousands)
Sq ft:
35
21
41
25
27
37
32
41
26
Price:
310
298
380
307
326
461
498
524
275
a.  Plot out the scatterplot of the data on the graph
below.  Be sure to label your axis with reasonable units and
label the units on each axis (ie, which is the sq ft and which is
the price)
b.  Does the data seem to be linearly related, and if so,
is the data related in a positive or negative way?
c.  What is the value of the correlation coefficient? 
What does that say about the data?
d.  Calculate the regression equation
e.  What does the slope of the regression line represent in
terms of size and the price of a homes in this area (use specific
numbers here)?
f.  Use the regression equation to determine the price of a
home in this area that has 2600 square feet.
g.  Use the regression equation to determine the square
footage of a house that is $375,000

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Added by James P.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Sheryl Ezze

01/15/2022

Step 1

Step 1: Plot the scatterplot of the data with square footage on the x-axis and price on the y-axis. Show more…

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The following table provides data for a sample of nine random homes sampled that compares the square footage of the home (in hundreds) and the price of the home (in thousands) Sq ft: 35 21 41 25 27 37 32 41 26 Price: 310 298 380 307 326 461 498 524 275 a. Plot out the scatterplot of the data on the graph below. Be sure to label your axis with reasonable units and label the units on each axis (ie, which is the sq ft and which is the price) b. Does the data seem to be linearly related, and if so, is the data related in a positive or negative way? c. What is the value of the correlation coefficient? What does that say about the data? d. Calculate the regression equation e. What does the slope of the regression line represent in terms of size and the price of a homes in this area (use specific numbers here)? f. Use the regression equation to determine the price of a home in this area that has 2600 square feet. g. Use the regression equation to determine the square footage of a house that is $375,000

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Transcript

00:01 So you have some data where you have the square footage, and these are in hundreds, and then you have the price in thousands.

00:12 And i'm not going to go through and make a scaled diagram.

00:17 I did a stat plot on my calculator, and the data appears to kind of look like this.

00:23 I'll kind of simulate what i see on mine, and i'm not going to put an access system on here.

00:31 But you'll have your square footage down here in hundreds and you'll have your price here.

00:37 And part b asks us to talk about, does this seem to have a linear relationship? yes, it does seem to be linear.

00:43 You know, moderately strong linear relationship with a positive association.

00:50 So that as x goes up, y also goes up.

00:55 So as the, as you would expect, as a square footage increases, it appears as though the price increases.

01:00 And then part c, we're asked to find the correlation coefficient.

01:04 It says nothing about doing it longhand.

01:06 So i'm going to use my linear regression on my calculator in order to calculate it.

01:11 And we're getting that r value to be 0 .68 roughly 5.

01:17 0 .685.

01:19 So it's not super strong.

01:21 It's like a moderately strong linear relationship.

01:24 Then we want to know what the regression equation is, and that is 93.

01:31 690 plus and we have a slope of 8 .8975 that would round to x.

01:41 That would be our linear regression line.

01:45 Part e asks us, oh, and i think we're also supposed to, then that's part d.

01:51 Part e we're supposed to discuss the slope.

01:54 And we know the slope is the change in y over the change in x, and that slope is that 8 .8975.

02:05 Roughly it is nine.

02:07 So it appears as though, and what of our units? well, our y unit is the dollars in thousands per square footage.

02:19 And so per square feet...

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