The coefficient of determination is represented by what notation?

The coefficient of determination is represented by what notation?

 

  r

 

  β

 

  ρ

 

  r2

 

Question 2(CO 6) Two variables have a negative linear correlation. Does the independent variable increase or decrease as the dependent variable increases?

 

  Independent variable decrease

 

  Independent variable would remain the same

 

  Cannot determine from information given

 

  Independent variable increases

 

Question 3(CO 6) Find the regression equation for the following data set

 

x          245       287       198       189       176       266       210       155

 

y          50         80        110      78        44        57        51        44

 

  ? = 45.69x – 0.69

 

  ? = 0.09x + 45.69

 

  ? = 45.69x + 0.09

 

  cannot be determined

 

Question 4(CO 6) A student wants to determine if a higher quality diet will improve their grade point average. Which variable would be the response variable?

 

  The student

 

  Their GPA

 

  The higher quality diet

 

  The number of classes taken

 

Question 5(CO 6) A value of the slope of the regression line would be given the notation of:

 

  m

 

  r

 

  r2

 

  b

 

Question 6(CO 6) A scatter plot generally shows the dots going from low y values and low x values, to high y values and high x values. Is the slope of the regression line between these two variables positive or negative?

 

  Positive. As one variable increases, the other decreases

 

  Negative. As one variable increases, the other decreases

 

  Positive. As one variable increases, so does the other

 

  Negative. As one variable increases, so does the other

 

Question 7(CO 6) If there is a (-), or bar, above a variable, what does that indicate?

 

  the value is the standard deviation

 

  the value is an estimate

 

  the value is the mean

 

  the value is an outlier

 

Question 8(CO 6) Find the regression equation for the following data set

 

x         7          8          5          9          4          10         2        

 

y          4          12         8          3          7          9          3

 

  ? = 0.39x + 4.08

 

  ? = -0.40x – 4.80

 

  ? = 0.40x + 4.08

 

  ? = 0.39x – 4.80

 

Question 9(CO 6) A data set whose original x values ranged from 28 through 49 was used to generate a regression equation of ? = 2.9x – 34.7. Use the regression equation to predict the value of y when x=24.

 

  51.2

 

  Meaningless result

 

  34.9

 

  91.2

 

Question 10(CO 6) A data set whose original x values ranged from 241 through 290 was used to generate a regression equation of ? = -0.06x + 9.8. Use the regression equation to predict the value of y when x=240.

 

  24.2

 

  4.6

 

  -4.6

 

  Meaningless result

 

Question 11(CO 6) A data set whose original x values ranged from 38 through 65 was used to general a regression equation of ? = -4.4x + 2.6. Use the regression equation to predict the value of y when x=62.

 

  -275.4

 

  -270.2

 

  Meaningless result

 

  275.4

 

Question 12

 

(CO 6) If the linear correlation coefficient is 0.822, what is the value of the coefficient of determination?

 

  -0.676

 

  0.907

 

  -0.907

 

  0.676

 

Question 13(CO 6) If the linear correlation coefficient is -0.256, what is the value of the coefficient of determination?

 

  0.512

 

  -0.512

 

  0.066

 

  -0.066

 

Question 14(CO 6) If the coefficient of determination is 0.792, what percentage of the data about the regression line is explained?

 

  20.8%

 

  30.8%

 

  30.2%

 

  79.2%

 

Question 15(CO 6) If the coefficient of determination is 0.618, what percentage of the data about the regression line is unexplained?

 

  68.1%

 

  30.2%

 

  38.2%

 

  61.8%

 

Question 16(CO 6) If the explanatory variables explained more than 20% of the variation in the response variables, which of the following would be true?

 

  There are two explanatory variables

 

  The coefficient of determination is below 0.2

 

  The coefficient of determination is above 0.2

 

  There are two response variables

 

Question 17(CO 6) The equation used to predict how tall a kitten will be as an adult is ? = 4.5 + 0.6×1 + 0.3×2, where x1 is the height of the sibling and x2 is the height of the mother. Use this equation to predict the height of a kitten whose sibling is 41.8 inches tall and whose mother is 49.2 inches tall.

 

  46.56 inches

 

  44.95 inches

 

  56.44 inches

 

  44.34 inches

 

Question 18(CO 6) The equation used to predict how many days it takes a 15-year old to read the first Harry Potter book is ? = 1.5 + 2.82×1 – 1.04×2 days, where x1 is the weekly hours of other activities and x2 is the reading grade level. Use this equation to predict how many days it will take to read this book for someone with 9.3 weekly hours of other activities and a 10.2 reading grade level.

 

  16.43 days

 

  18.52 days

 

  20.59 days

 

  17.12 days