VCE Further Maths Cambridge Ch4 Review

In the least squares regression line y = –5.6 – 0.78x

• the y-intercept = –5.6 and slope = 0.78

• the y-intercept = –5.6 and slope = –0.78

• the y-intercept = 5.6 and slope = 0.78

• the y-intercept = –0.78 and slope = –5.6

• the y-intercept = 0.78 and slope = 5.6

If the equation of a least squares regression line is y = –5.6 – 0.78x and r^2 = 0.48

• r = –0.69

• r = –0.48

• r = 0.23

• r = 0.48

• r = 0.69

The least squares regression line y = –5.6 – 0.78x predicts that, when x = 10, the value of y is:

• –13.4

• –7.8

• –2.2

• 7.8

• 13.4

Using a least squares regression line, the predicted value is 15.4. The actual data value is 17.8. The residual value is:

• –2.4

• 0.9

• 1.2

• 2.4

• 33.2

The equation of the least squares line plotted on the scatterplot below is closest to:

• y = 19 – x

• y = 19.5 – x

• y = 20 – x

• y =19 – 1.25x

• y = 19.5 –1.25 x

The number of mistakes made proofreading can be predicted from the time spent (in minutes) completing the task using the least squares regression line:  $number\ ofmistakes=8.5–0.1\times time$  with r = –0.4170
Which of the following statements relating to the regression line is true?

• The slope of the regression line is 8.5. 

• The explanatory variable in the regression equation is number of mistakes.

• The least squares line passes through the origin

• The intercept is –0.1. 

• The equation predicts that a person who completes the proofreading task in 35 minutes will make 5 mistakes.

The number of mistakes made proofreading can be predicted from the time spent (in minutes) completing the task using the least squares regression line:  
 $numberofmistakes=8.5–0.1\times time$ 
This regression line predicts that, on average, the number of mistakes made proofreading:  

• decreases by 8.5 for each additional minute spent completing the task

• increases by 8.5 for each additional minute spent completing the task

• decreases by 7.5 for each additional minute spent completing the task

•  decreases by 0.1 for each additional minute spent completing the task

• increases by 0.1 for each additional minute spent completing the task

The number of mistakes made proofreading can be predicted from the time spent (in minutes) completing the task using the least squares regression line:  $numberofmistakes=8.5–0.1\times time$  
A person who takes 45 minutes to complete the proofreading task made 5 errors. If the regression equation is used to predict the number of mistakes they are expected to make then the residual value will be closest to: 

• -3

• -1

• 1

• 3

• 4

The association between blood glucose level and weight can be described as:

• non-linear

• weak, positive, linear

• weak, negative, linear

• strong, positive, linear with an outlier

• strong, negative, linear with an outlier

The association between mistakes made and time taken could be described as:

• weak, positive, linear

• weak, negative, linear

• non-linear

• strong, positive, linear

• strong, negative, linear