MATH 221 Week 7 Quiz 1

MATH 221 Week 7 Quiz 1 | Devry University

Question 1

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

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

·         Dependent variable decreases  

·         Dependent variable would remain the same    

·         Dependent variable increases  

·         Cannot determine from information given 

 

Question 2

What does the variable ρ represent?

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

·         The population correlation coefficient  

·         The sample correlation coefficient  

·         The coefficient of determination  

·         The critical value for the correlation coefficient

 

 Question 3

A baseball player wants to determine if the type of bat he uses each year can be used to predict the amount of improvement in his game. Which variable would be the explanatory variable?

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

·         The baseball player  

·         The improvement in his game  

·         The number of times he bats   

·         The type of bat

 

 Question 4

What would be the notation for the mean of the y values?

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

·         yi  

·         b    

·         y̅  

·         (x, y)

 

 Question 5

Which of the following graphs displays the regression equation of ŷ=1.41x + 3.16?

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

 

 Question 6

Find the regression equation for the following data set

x              142         167         143         189         175         174         134         155

y              20          80          72          69          44          59          51          63

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

·         ŷ = 0.33x + 3.70  

·         ŷ = 0.33x – 3.70  

·         cannot be determined  

·         ŷ = -0.33x + 3.70

 

 Question 7

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.

Homework Help:

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

·         318.7  

·         451.2  

·         391.2  

·         Meaningless result

 

Question 8

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=110.

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

·         Meaningless result  

·         -7.6  

·         20.80  

·         21.34

 

Question 9

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

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

·         -726.0    

·         -624.0 

·         Meaningless result  

·         624.0

 

 Question 10

If the linear correlation coefficient is -0.654, what is the value of the coefficient of determination?

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

·         0.308  

·         -0.428    

·         0.428  

·         0.654

 

 Question 11

If the coefficient of determination is 0.497, what percentage of the variation in the data about the regression line is explained?

7DG. Interpreting the coefficient of determination (Links to an external site.) (DOCX)  

·         24.7% 

·         50.0%   

·         49.7%  

·         50.3%

 

 Question 12

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

7DG. Interpreting the coefficient of determination (Links to an external site.) (DOCX)  

·         6.7.6%  

·         82.2%    

·         17.8%  

·         32.2%

 

Question 13

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

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

·         There are two independent variables  

·         The coefficient of determination is below 0.5  

·         There are two dependent variables    

·         The coefficient of determination is above 0.5

 

 Question 14

The equation used to predict how tall a dog will be as an adult is ŷ=4.5 + 0.7x1 + 0.55x2, 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 42.8 inches tall and whose father is 47.1 inches tall.

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

·         60.37 inches  

·         55.87 inches  

·         44.95 inches  

·         61.01 inches 

 Question 15

The equation used to predict how long a cold will last is ŷ=-1.8 + 0.09x1 + 3.2x2 – 1.9x3, 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 100.8 degrees, an average of 3 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)  

·         7.3 days  

·         5.8 days    

·         5.5 days  

·         8.7 days