1.

Student: _____________________Date: _____________________

Instructor: Doug EnsleyCourse: Applied Statistics - Ensley 03/04 Assignment: Online F - Lesson 3

(1) positive negative

(2) decrease increase

For the response variable y, the selling price in thousands of dollars, and the expanatory variable x, the size of the house in thousands of square feet, x.y = 9.9 + 76.5a. How much do you predict a house would sell for if it has (i) 2000 square feet, (ii) 3000 square feet?b. Using results in part a, explain how to interpret the slope.c. Is the correlation between these variables positive or negative? Why?d. One home that is 3000 square feet sold for $300,000. Find the residual, and interpret.

a. (i) The predicted selling price of a house that has 2000 square feet is $ .

(ii) The predicted selling price of a house that has 3000 square feet is $ .

b. Which of the following statements best interprets the slope?

A. For every increase of $1000 in selling price, the predicted size of the house decreases by square feet.76,500

B. For every increase of 1000 square feet to house size, the predicted selling price decreases by $ .76,500

C. For every increase of 1000 square feet to house size, the predicted selling price increases by $ .76,500

D. For every increase of $1000 in selling price, the predicted size of the house increases by square feet.

76,500

c. The correlation is (1) because the selling price tends to (2) as the house size increases.

d. The residual is $ .

Which of the following statements best interprets this residual?

A. The selling price of this particular house is greater than the predicted value by the amount of the residual.

B. The residual is the predicted selling price for houses with zero square feet.

C. The residual is the amount the predicted selling price of houses increases for each increase of 1000 square feet.

D. The selling price of this particular house is less than the predicted value by the amount of the residual.

2.

(1) d c a b

(2) b a c d

(3) b c a d

(4) d c b a

Match the scatterplots to the right with the correlation values.1. r = 02. r = − 0.973. r = 0.584. r = 1

1. Scatterplot (1)

2. Scatterplot (2)

3. Scatterplot (3)

4. Scatterplot (4)

(a)

(b)

(c)

(d)

*3.

1: Scatterplots

The accompanying scatterplots concern the total assessed value of properties that include homes, and both depict the same observations. Complete parts (a) and (b) below.

Click the icon to view the scatterplots.1

a. Which do you think has a stronger relationship with value of the property the number of square feet in the home or the number of fireplaces in the home? Why?

—

A. The number of square feet has a stronger relationship with the value of the property, as shown by the fact that the points are more scattered in a vertical direction.

B. The number of square feet has a stronger relationship with the value of the property, as shown by the fact that the points are less scattered in a vertical direction.

C. The number of fireplaces has a stronger relationship with the value of the property, as shown by the fact that the points are more scattered in a vertical direction.

D. The number of fireplaces has a stronger relationship with the value of the property, as shown by the fact that the points are less scattered in a vertical direction.

b. If you were trying to predict the value of a property (where there is a home) in this area, would you be able to make a better prediction by knowing the number of square feet or the number of fireplaces? Explain. Choose the correct answer below.

A. Square feet. Total value is more strongly associated with square feet, because there is less variability in total value for any given value of square feet.

B. Fireplaces. Total value is more strongly associated with fireplace, because there is less variability in total value for any given value of number of fireplaces.

C. Neither because the association is the same between the value of property and square feet and the value of property and the number of fireplaces.

*4.

*5.

*6.

The figure shows a scatterplot of the age of students and the value of their cars. Does it show an increasing trend, a decreasing trend, a changing trend, or very little trend?

Age of Student

Valu

e of

Car

(dol

lars

)

Choose the correct answer below.

trendchanging

trendincreasing

trenddecreasing

trendno

(1) no a decreasing an increasing

(2) a decreasing an increasing

no

(3) is not is

(4) do not show show

The figure shows a scatterplot of shoe size and GPA for some college students. Does it show an increasing trend, a decreasing trend, or no trend? Is there a strongrelationship?

5 6 7 8 9 10 11122.0

2.5

3.0

3.5

4.0

Shoe Size

GPA

The graph shows (1) linear trend since the points show (2) pattern by scanning the

graph from left to right. The relationship (3) strong because the points (4) consistent and small vertical spread.

The scatterplot shows the actual weight and desired weight change of some students. Thus, if they weighed 220 and wanted to weigh 190, the desired weight change would be negative 30. Explain what you see. In particular, what does it mean that the trend is negative?

Choose the correct answer below.

A. The less people weigh, the more weight they tend to want to lose.

B. The more people weigh, the less weight they tend to want to lose.

C. The more people weigh, the more weight they tend to want to lose.

*7.

*8.

*9.

The scatterplot to the right shows the number of hours of work per week and the number of hours of sleep per night for some college students. Does the graph show a strong increasing trend, a strong decreasing trend, or very little trend? Explain.

0 20 40 60 80456789

1011

Work Hours

Sle

ep H

ours

Does the graph show an increasing trend, a decreasing trend, or no trend? Choose the correct answer below.

trendvery little

trenddecreasing

trendincreasing

Explain. Choose the correct answer below.

A. The number of hours of work does not seem to be related to the number of hours of sleep for these students.

B. The number of hours of work is less than or equal to the number of hours of sleep for these students.

C. Students who work more hours tend to get fewer hours of sleep.

D. Students who work more hours tend to also get more hours of sleep.

(1) a negative association no association

a positive association a scattered association

Fill in the blank.

Since, in general, the longer a car is owned the more miles it travels one can say there is a _______ between age of a car and mileage.

Since, in general, the longer a car is owned the more miles it travels one can say there is (1) between age of a car and mileage.

(1) non-linear. negative. strong. weak.

Fill in the blank.

A large amount of scatter in a scatterplot is an indication that the association between the two variables is _______.

A large amount of scatter in a scatterplot is an indication that the association between the two variables is

(1)

*10.

*11.

Complete parts (a) and (b) below.

a. The scatterplot to the right shows the college tuition and percentage acceptance at some colleges. Would it make sense to find the correlation using this data set? Why or why not?

A. No. Linear regression is not appropriate because the trend is not linear.

B. Yes. There is no reason why linear regression would not be appropriate because the trend is linear.

C. No. Linear regression is not appropriate because there are not enough data points.

D. Yes. There is no reason why linear regression would not be appropriate because there is a large number of data points.

10 15 20 25 30 35 40 45102030405060708090

100

College Tuition (thousands of dollars)

Per

cent

Acc

epta

nce

b. The scatterplot to the right shows the composite grade on the ACT (American College Testing) exam and the English grade on the same exam. Would it make sense to find the correlation using this data set? Why or why not?

A. No. Linear regression is not appropriate because there are not enough data points.

B. Yes. There is no reason why linear regression would not be appropriate because the trend is linear.

C. No. Linear regression is not appropriate because the trend is not linear.

D. Yes. There is no reason why linear regression would not be appropriate because there is a large number of data points.

10 15 20 25 30 3515.0

17.5

20.0

22.5

25.0

27.5

30.0

32.5

English Score on the ACT Exam

Com

posi

te S

core

on

the

AC

T E

xam

A professor went to a website for rating professors and looked up the quality rating and also the "easiness" of the six full-time professors in one department. The ratings are 1 (lowest quality) to 5 (highest quality) and 1 (hardest) to 5 (easiest). The numbers given are averages for each professor. Assume the trend is linear, find the correlation, and comment on what it means.

Quality Easiness 4.8   3.74.5 3.24.3 3.44.1 2.73.9 1.93.6 1.9

Calculate the correlation.

r (Round to three decimal places as needed.)=

Comment on the meaning of the correlation. Choose the correct interpretation below.

A. The professors that have high easiness scores tend to also have high quality scores.

B. Being "easy" as a professor causes students to regard the professor as having a lower quality.

C. The professors that have high easiness scores tend to also have low quality scores.

D. Being "easy" as a professor causes students to regard the professor as having a higher quality.

*12.

*13.

*14.

(1) coefficient of determination correlation constant

correlation coefficient association coefficient

Fill in the blank.

The _______ is a number that measures the strength of the linear association between two numerical variables.

The (1) is a number that measures the strength of the linear association between two numerical variables.

(1)

Fill in the blank.

The correlation coefficient is always a number between _______.

The correlation coefficient is always a number between (1)

0 and 1.− 1 and 1.0 and 10.− 10 and 0.

When can a correlation coefficient based on an observational study be used to support a claim of cause and effect?

Choose the correct answer below.

A. When the correlation coefficient is equal to 1 or 1.− +

B. When the scatterplot of the data has little vertical variation.

C. When the correlation coefficient is close to 1 or 1.− +

D. Never

*15. The scatterplot shows the median annual pay, in dollars per year, forcollege-educated men and women in 30 cities. The correlation is . The regression equation is shown below. Complete parts a and b.

0.835

Predicted Women = 13,250 + 0.5227 Men

40000 60000 8000030000

40000

50000

60000

Men's Median Pay

Wom

en's

Med

ian

Pay

a. Find a rough estimate (by using the scatterplot) of median pay for women in a city that has a median pay of about $ for men.60,000

A. Between $ and $40,000 50,000

B. Between $ and $50,000 60,000

C. Between $ and $30,000 40,000

D. Between $ and $60,000 70,000

b. Use the given regression equation to get a more precise estimate of the median pay for women in a city that has a median pay for men of $ .60,000

The estimated median pay for women is $ .

16.

(1) a strong positive a moderate negative

no a strong negative

a moderate positive (2) a strong negative a moderate positive

a strong positive a moderate negative

(3) higher lower

A graduate teaching assistant for an Introduction to Statistics course collected data from one of her classes to investigate the relationship between using the explanatory variable x study time per week (average number of hours) to predict the response variable y college GPA. For the 21 females in her class, the correlation was 0.42. For the eight males in herclass, the data were as shown in the following table. Complete parts a through c below.

==

Student 1 2 3 4 5 6 7 8 Study Time 22 14 26 14 5 11 9 5GPA 3.9 2.8 3.7 3.5 2.6 3.2 3.1 2.8

a. Construct a scatterplot. Interpret.

Which scatterplot below correctly shows the data?

A.

0 400

4

x

y

B.

0 400

4

x

y

C.

0 400

4

x

y

D.

0 400

4

x

y

The scatterplot shows (1) association between the two variables.

b. Find and interpret the correlation.

The correlation is .(Round to two decimal places as needed.)

The correlation shows (2) association between the two variables, with longer study times associated with

(3) GPAs.

c. Find and interpret the prediction equation by reporting the predicted GPA for a student who studies (i) hours per week, (ii) hours per week.

626

The regression equation is x.y = +(Round to two decimal places as needed.)

The predicted GPA for a student who studies hours per week is .6((Round to two decimal places as needed.)

The predicted GPA for a student who studies hours per week is .26(Round to two decimal places as needed.)

17.

(1) a moderate positive a strong positive

no a strong negative

a moderate negative (2) weight cost

(3) pound, dollar,

(4) weight cost

(5) decrease increase

(6) pounds. dollars.

(7) weight of a mountain bike that costs $0. cost of a mountain bike that weighs 0 pounds.

(8) are no are

(9) has does not have

Is there a relationship between the weight and price of a mountain bike? The following data set gives the weights and prices for ten mountain bikes. Let the expanatory variable x be the weight in pounds and the response variable y be thebike's price.

Weight (LB) 31 30 29 29 30 37 35 35 28 33 Price ($) 1020 1100 700 440 570 160 920 190 590 350

a. Construct a scatterplot. Interpret.b. Find the regression equation. Interpret the slope in context. Does the y-intercept have contextual meaning?c. You decide to purchase a mountain bike that weighs pounds. What is the predicted price for the bike?30

a. Which scatterplot below correctly shows the data?

A.

25 400

1200

x

y

B.

25 400

1200

x

y

C.

25 400

1200

x

y

D.

25 400

1200

x

y

The scatterplot shows (1) association between the two variables.

b. The regression equation is x.y = +(Round to two decimal places as needed.)

The slope means that as the (2) of a mountain bike increases by one (3) the

(4) tends to (5) by (6)

The y-intercept is the (7) Since there (8) observations with such x-values, the y-intercept

(9) contextual meaning.

c. The predicted price of a mountain bike that weighs pounds is $ .30(Round to the nearest cent as needed.)

1. 162,900

239,400

C. For every increase of 1000 square feet to house size, the predicted selling price increases by $ .76,500

(1) positive

(2) increase

60,600

A. The selling price of this particular house is greater than the predicted value by the amount of the residual.

2. (1) d

(2) a

(3) c

(4) b

3. B. The number of square feet has a stronger relationship with the value of the property, as shown by the fact that the points are less scattered in a vertical direction.

A. Square feet. Total value is more strongly associated with square feet, because there is less variability in total value for any given value of square feet.

4. trendno

5. (1) an increasing

(2) an increasing

(3) is

(4) show

6. C. The more people weigh, the more weight they tend to want to lose.

7. trendvery little

A. The number of hours of work does not seem to be related to the number of hours of sleep for these students.

8. (1) a positive association

9. (1) weak.

10. A. No. Linear regression is not appropriate because the trend is not linear.

B. Yes. There is no reason why linear regression would not be appropriate because the trend is linear.

11. 0.933

A. The professors that have high easiness scores tend to also have high quality scores.

12. (1) correlation coefficient

13. (1) − 1 and 1.

14. D. Never

15. A. Between $ and $40,000 50,000

44,612

16.

A. 0 400

4

x

y

(1) a strong positive

0.86

(2) a strong positive

(3) higher

2.50

0.05

2.82

3.87

17.

A. 25 400

1200

x

y

(1) a moderate negative

2020.74

− 44.69

(2) weight

(3) pound,

(4) cost

(5) decrease

44.69

(6) dollars.

(7) cost of a mountain bike that weighs 0 pounds.

(8) are no

(9) does not have

679.98