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Week 7 Homework

Question 1Two variables have a negative non-linear correlation. Does the dependent variable increase or decrease as the independent variable increases?

Homework Help:

7DA. Linear, non-linear, positive and negative correlations (Links to an external site.) (PDF)

Dependent variable decreases

Dependent variable increases

Cannot determine from information given

Dependent variable would remain the same

Question 2What does the variable r represent?

Homework Help:

7DB. Correlation coefficient and coefficient of determination, notation and meanings (Links to an external site.) (PDF)

The coefficient of determination

The sample correlation coefficient

The population correlation coefficient

The critical value for the correlation coefficient

Question 3A golfer wants to determine if the type of driver she uses each year can be used to predict the amount of improvement in her game. Which variable would be the explanatory variable?

Homework Help:

7DA. Linear, non-linear, positive and negative correlations (Links to an external site.) (PDF)

7DC. Explanatory and response variables (Links to an external site.) (PDF)

The number of holes she plays

The improvement in her game

The type of driver

The rating of the golfer

Question 4Two variables have a positive linear correlation. Where would the y-intercept of the regression line be located on the y-axis?

Homework Help:

7DA. Linear, non-linear, positive and negative correlations (Links to an external site.) (PDF)

Below 0

To the left of 0

Cannot determine

To the right of 0

Question 5A value of the dependent variable that corresponds to the value of xi would be given the notation of:

Homework Help:

7DD. Regression notation of m, b, y1, x1, yi, xi, means of variables, estimates of variables (Links to an external site.) (PDF)

y1

b

m

yi

Question 6If there is a ^, or hat, above a variable, what does that mean?

Homework Help:

7DD. Regression notation of m, b, y1, x1, yi, xi, means of variables, estimates of variables (Links to an external site.) (PDF)

the value is an outlier

the value is the standard deviation

the value is an estimate

the value is the mean

Question 7Which of the following graphs displays the regression line of ?=0.75x + 3.34?

Homework Help:

7VA. Scatter plots with regression lines, slope and intercept (Links to an external site.) (2:32)

Scatter plot generally from upper left to lower right where y-intercept is estimated to be around 7

Scatter plot generally from lower left to upper right where y-intercept is estimated to be around 40

Scatter plot generally from upper left to lower right where y-intercept is estimated to be around 7

Scatter plot generally from lower left to upper right where y-intercept is estimated to be around 3

Question 8Find the regression equation for the following data set

x 143 167 143 189 122 174 134 155

y 60 80 72 69 44 59 51 63

Homework Help:

7VB. Finding regression line equation using spreadsheet (Links to an external site.) (3:54)

12.16x + 0.33

0.33x + 12.16

12.16x – 0.33

cannot be determined

Question 9A data set whose original x values ranged from 41 through 78 was used to generate a regression equation of ?=5.3x – 21.9. Use the regression equation to predict the value of y when x=81.

Homework Help:

7VC. Validity of regression equation to estimate y from values of x (Links to an external site.) (3:00)

391.2

451.2

318.7

Meaningless result

Question 10A data set whose original x values ranged from 120 through 351 was used to generate a regression equation of ?=0.06x + 14.2. Use the regression equation to predict the value of y when x=119.

Homework Help:

7VC. Validity of regression equation to estimate y from values of x (Links to an external site.) (3:00)

21.40

21.34

-7.06

Meaningless result

Question 11Find the regression equation for the following data set

x 7 8 5 9 4 3 9 6 7 8

y 4 2 8 3 7 9 3 5 6 9

Homework Help:

7VB. Finding regression line equation using spreadsheet (Links to an external site.) (3:54)

11.20x – 0.85

-11.20x – 0.85

0.85x + 11.20

-0.85x + 11.20

Question 12

A data set whose original x values ranged from 137 through 150 was used to general a regression equation of ?=-4.5x + 51. Use the regression equation to predict the value of y when x=139.

Homework Help:

7VC. Validity of regression equation to estimate y from values of x (Links to an external site.) (3:00)

-547.5

-574.5

Meaningless result

574.5

Question 13If the linear correlation coefficient is 0.661, what is the value of the coefficient of determination?

Homework Help:

7DB. Correlation coefficient and coefficient of determination, notation and meanings (Links to an external site.) (PDF)

1.322

0.437

0.661

-0.437

Question 14If the linear correlation coefficient is -0.471, what is the value of the coefficient of determination?

Homework Help:

7DB. Correlation coefficient and coefficient of determination, notation and meanings (Links to an external site.) (PDF)

0.1942

0.222

-0.942

-0.222

Question 15If the coefficient of determination is 0.184, what percentage of the data about the regression line is explained?

Homework Help:

7DB. Correlation coefficient and coefficient of determination, notation and meanings (Links to an external site.) (PDF)

18.4%

3.39%

24.2%

36.8%

Question 16If the coefficient of determination is 0.298, what percentage of the data about the regression line is unexplained?

Homework Help:

7DB. Correlation coefficient and coefficient of determination, notation and meanings (Links to an external site.) (PDF)

6.9%

26.2%

73.8%

70.2%

Question 17If the independent variables explained less than 50% of the variation in the dependent variables, which of the following would be true?

Homework Help:

7DE. Compare linear regression and multiple regression (Links to an external site.) (PDF)

There are two dependent variables

The coefficient of determination is below 0.5

The coefficient of determination is above 0.5

There are two independent variables

Question 18The equation used to predict how tall a dog will be as an adult is ?=4.5 + 0.7×1 + 0.55×2, where x1 is the height of the mother and x2 is the height of the father. Use this equation to predict the height of a puppy whose mother is 40.3 inches tall and whose father is 45.9 inches tall.

Homework Help:

7DF. Using a multiple regression equation to estimate values from independent variable values (Links to an external site.) (PDF)

50.75 inches

53.46 inches

43.10 inches

57.96 inches

Question 19The equation used to predict how long it will take to receive a package through the mail is ?=0.5 + 0.02×1 + 0.85×2

days, where x1 is the distance to travel and x2 is the weight of the package. Use this equation to predict the how long it will take to receive a package that is 224 miles away and weighs 2.2 pounds.

7DF. Using a multiple regression equation to estimate values from independent variable values (Links to an external site.) (PDF)

190.9 days

113.1 days

6.9 days

6.4 days

Question 20The equation used to predict how long a cold will last is ?=-1.8 + 0.09×1 + 3.2×2 – 1.9×3, where x1

is person’s temperature on the first day, x2 is number of people seen each day, and x3 is the amount of sleep the person gets. Use this equation to predict how long a cold will last with a temperature of 101.4 degrees, an average of 4 people seen each day, and 6 hours of sleep.

7DF. Using a multiple regression equation to estimate values from independent variable values (Links to an external site.) (PDF)

8.7 days

9.5 days

10.5 days

9.7 days