2. Hanna Properties specializes in custom home resales in the Equestrian Estates, an exclusive subdivision in Phoenix, Arizona. A random sample of nine custom homes currently listed for sale provided the following information on size and price. Here, x denotes size, in hundreds of square feet, rounded to the nearest hundred, and y denotes price, in thousands of dollars, rounded to the nearest thousand. For part (g), predict the price of a 2600-sq. ft. home in the Equestrian Estates. 26 27 33 29 29 34 30 40 22 y 540 555 575 577 606 661 738 804 496 a) Find the regression equation for the data points. b) Graph the regression equation and the data points. c) Describe the apparent relationship between the two variables under consideration.

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2. Hanna Properties specializes in custom home resales in the Equestrian
Estates, an exclusive subdivision in Phoenix, Arizona. A random sample of nine
custom homes currently listed for sale provided the following information on
size and price. Here, x denotes size, in hundreds of square feet, rounded to the
nearest hundred, and y denotes price, in thousands of dollars, rounded to the
nearest thousand. For part (g), predict the price of a 2600-sq. ft. home in the
Equestrian Estates.
26
27
33
29
29
34
30
40
22
y
540
555
575
577
606
661
738
804
496
a) Find the regression equation for the data points.
b) Graph the regression equation and the data points.
c) Describe the apparent relationship between the two variables under
consideration.
d) Identify the predictor and response variables.
e) Identify outliers and potential influential observations.
f) Predict the values of the response variable for the specified values of the
predictor variable, and interpret your results.
3. Construct a scatter plot for the data in the folowing table
0.5
'1.5
y
2
1
3
a) Plot the following two lines on the scatter plot:
y = 3 – x and y = 1+ x
b) Which of these lines would you choose t0 characterize the relationship between
x and y? Explain
c) Show that the SSE for both these lines equals 0.
d) Which of these lines has the smaller SSE?
e) Find the least squares line for the data and compare it to the two lines described
in part a.
4. Suppose the data is given in the following table
2
4
3
y
3
7
a) Find the regression equation for the data points.
b) Graph the regression equation and the data points.
c) Compute the three sums of squares, SST,SSR, and SSE, using the defining
formulas.
d) Verify the regression identity, SST = SSR + SSE.
e) Compute the coefficient of determination.
f) Determine the percentage of variation in the observed values of the response
variable that is explained by the regression.
g) State how useful the regression equation appears to be for making predictions.
h) Determine the standard error of the estimate.
Transcribed Image Text:2. Hanna Properties specializes in custom home resales in the Equestrian Estates, an exclusive subdivision in Phoenix, Arizona. A random sample of nine custom homes currently listed for sale provided the following information on size and price. Here, x denotes size, in hundreds of square feet, rounded to the nearest hundred, and y denotes price, in thousands of dollars, rounded to the nearest thousand. For part (g), predict the price of a 2600-sq. ft. home in the Equestrian Estates. 26 27 33 29 29 34 30 40 22 y 540 555 575 577 606 661 738 804 496 a) Find the regression equation for the data points. b) Graph the regression equation and the data points. c) Describe the apparent relationship between the two variables under consideration. d) Identify the predictor and response variables. e) Identify outliers and potential influential observations. f) Predict the values of the response variable for the specified values of the predictor variable, and interpret your results. 3. Construct a scatter plot for the data in the folowing table 0.5 '1.5 y 2 1 3 a) Plot the following two lines on the scatter plot: y = 3 – x and y = 1+ x b) Which of these lines would you choose t0 characterize the relationship between x and y? Explain c) Show that the SSE for both these lines equals 0. d) Which of these lines has the smaller SSE? e) Find the least squares line for the data and compare it to the two lines described in part a. 4. Suppose the data is given in the following table 2 4 3 y 3 7 a) Find the regression equation for the data points. b) Graph the regression equation and the data points. c) Compute the three sums of squares, SST,SSR, and SSE, using the defining formulas. d) Verify the regression identity, SST = SSR + SSE. e) Compute the coefficient of determination. f) Determine the percentage of variation in the observed values of the response variable that is explained by the regression. g) State how useful the regression equation appears to be for making predictions. h) Determine the standard error of the estimate.
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