correlation coefficient

12 Oct correlation coefficient

Question 1 2 pts

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

Dependent variable would remain the same

Dependent variable increases

Dependent variable decreases

Cannot determine from information given

Question 2 2 pts

What does the variable p represent?

The sample correlation coefficient

The population correlation coefficient

The critical value for the correlation coefficient

The coefficient of determination

Question 3 2 pts

A 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?

The improvement in her game

The rating of the golfer

The type of driver

The number of holes she plays

Question 4 2 pts

Two variables have a negative linear correlation. Is the slope of the regression line between these two variables positive or negative?

Negative. As one variable increases, so does the other

Negative. As one variable increases, the other decreases

Positive. As one variable increases, the other decreases

Positive. As one variable increases, so does the other

Question 5 2 pts

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

M

b

yi

y1

Question 6 2 pts

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

the value is an   estimate

the value is an   outlier

the value is the   mean

the value is the   standard deviation

Question 7 2 pts

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

Question 8 2 pts

Find the regression equation for the following data set

x 123 146 127 161 122 174 134 155

y 80  51 59 41  44   59   51 63

-0.13x + 74.50

0.13x – 74.50

cannot be determined

74.50x – 0.13

Question 9 2 pts

A data set whose original x values ranged from 41 through 78 was used to generate a regression equation of ŷ=5.3x – 21.9. Use the regression equation to predict the value of y when x=81. 451.2

Meaningless result

391.2

318.7

451.2

Question 10 2 pts

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

21.40

21.34

Meaningless result

-7.06

Question 11 2 pts

Find the regression equation for the following data set

x 7 8 5  9 4 10 9 6 7 8

y 4 2 8 3 7 9 3 5 6 3

0.40x – 7.96

-0.40x – 7.96

0.40x–7.96

-0.40x – 7.96

Question 12 2 pts

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

-547.5

Meaningless result

574.5

-574.5

Question 13 2 pts

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

1.322

-0.437

0.437

0.661

Question 14 2 pts

If the linear correlation coefficient is -0.156, what is the value of the coefficient of determination?

0.312

0.024

-0.024

-0.312

Question 15 2 pts

If the coefficient of determination is 0.492, what percentage of the data about the regression line is explained?

49.2%

50.8%

70.1%

24.2%

Question 16 2 pts

If the coefficient of determination is 0.822, what percentage of the data about the regression line is unexplained?

32.2%

17.8%

6.76%

82.2%

Question 17 2 pts

If the independent variables explained about 50% of the variation in the dependent variables, which of the following would be true?

There are two independent variables

The coefficient of determination is above 0.5

There are two dependent variables

The coefficient of determination is below 0.5

Question 18 2 pts

The equation used to predict how tall a dog will be as an adult is ŷ=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.

57.96 inches

53.46 inches

50.75 inches

43.10 inches

Question 19 2 pts

The equation used to predict how long it will take to receive a package through the mail is ŷ=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 249 miles away and weighs 2.1 pounds.

1.6 days

7.8 days

6.8 days

7.3 days

Question 20 2 pts

The equation used to predict how long a cold will last is ŷ=-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.

10.5 days

8.7 days

9.5 days

9.7 days