(mg/dl) a) Construct a scatter diagram for these data. Does the scatter diagram exhibit a linear relationship between distance run and blood sugar level? b) Find the predictive regression equation of blood sugar level on the distance run. c) Give a brief interpretation of the values of Bo and ß1 calculated in part b.

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05:51 O O M •
Vo) 4G
LTÉ ll
TUTORIAL 1.pdf
1. A diabetic is interested in determining how the amount of aerobic exercise
impacts his blood sugar. When his blood sugar reaches 170 mg/dL, he goes
out for a run at a pace of 10 minutes per mile. On different days, he runs
different distances and measures his blood sugar after completing his run.
Note: The preferred blood sugar level is in the range of 80 to 120 mg/dL. Levels
that are too low or too high are extremely dangerous. The data generated are
given in the following table.
Distance 2
|2
2.5 2.5 3
3
3.5 3.5 4 4
4.5 4.5
(miles)
Blood
136 | 146 131
125 120 116 104 95 85 94 83
75
sugar
(mg/dl)
a) Construct a scatter diagram for these data. Does the scatter diagram exhibit a
linear relationship between distance run and blood sugar level?
b) Find the predictive regression equation of blood sugar level on the distance run.
c) Give a brief interpretation of the values of ßo and B, calculated in part b.
d) Plot the predictive regression line on the scatter diagram of part a and show the
errors by drawing vertical lines between scatter points and the predictive
regression line.
e) Calculate the predicted blood sugar level count after a run of 3.1 miles (5
kilometers).
f) Estimate the blood sugar level after a 10-mile run. Comment on this finding.
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 following table
0.5
1
*1.5
y
2
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 batween
: und y? Explain
c) Show that the SSE for both these lines equals 0.
Transcribed Image Text:05:51 O O M • Vo) 4G LTÉ ll TUTORIAL 1.pdf 1. A diabetic is interested in determining how the amount of aerobic exercise impacts his blood sugar. When his blood sugar reaches 170 mg/dL, he goes out for a run at a pace of 10 minutes per mile. On different days, he runs different distances and measures his blood sugar after completing his run. Note: The preferred blood sugar level is in the range of 80 to 120 mg/dL. Levels that are too low or too high are extremely dangerous. The data generated are given in the following table. Distance 2 |2 2.5 2.5 3 3 3.5 3.5 4 4 4.5 4.5 (miles) Blood 136 | 146 131 125 120 116 104 95 85 94 83 75 sugar (mg/dl) a) Construct a scatter diagram for these data. Does the scatter diagram exhibit a linear relationship between distance run and blood sugar level? b) Find the predictive regression equation of blood sugar level on the distance run. c) Give a brief interpretation of the values of ßo and B, calculated in part b. d) Plot the predictive regression line on the scatter diagram of part a and show the errors by drawing vertical lines between scatter points and the predictive regression line. e) Calculate the predicted blood sugar level count after a run of 3.1 miles (5 kilometers). f) Estimate the blood sugar level after a 10-mile run. Comment on this finding. 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 following table 0.5 1 *1.5 y 2 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 batween : und y? Explain c) Show that the SSE for both these lines equals 0.
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