Chapter 3 - Linear Associations Unit 3

In a study of the association between a person's height, in centimetres and body surface area, in square metres, the following least squares regression line was obtained.

body surface area = -1.1 + 0.019 x height

Which one of the following is correct?

• An increase of 1 m² in body surface area is associated with an increase of 0.019 cm in height.

• An increase of 1 cm in height is associated with an increase of 0.019 m² in body surface area.

• The correlation coefficient is 0.019

• A person's body surface area, in square metres, can be determined by adding 1.1 cm to their height

• A person's height, in cm, can be determined by subtracting 1.1 from their body surface area, in square metres.

This equation is used to predict the value of y when x = 1.1.

The value of y is closest to

• -0.24

• 0.57

• 0.91

• 1.6

• 3.7

Using this least squares line to model the association between resting pulse rate and time spent exercising, the residual for the student who spent four hours per week exercising is closest to

• -2.0 beats per minute

• -1.0 beats per minute

• -0.3 beats per minute

• 1.0 beats per minute

• 2.0 beats per minute

The equation of this least squares line is closest to

• resting pulse rate = 67.2 - 0.91 x time spent exercising

• resting pulse rate = 67.2 - 1.10 x time spent exercising

• resting pulse rate = 68.3 - 0.91 x time spent exercising

• resting pulse rate = 68.3 - 1.10 x time spent exercising

• resting pulse rate = 67.2 + 0.91 x time spent exercising

Using this information, the value of the correlation coefficient r for this set of bivariate data is closest to

• 0.88

• 0.89

• 0.92

• 0.94

• 0.97

The heights of a group of children between one and six years old were measured.

The least squares regression line for height in cm and age in years is shown below:

height = 58.22 + 10.46 x age

How tall is a child predicted to be when they are born?

• 58.22 cm

• 10.46 cm

• 102.45 cm

• 5.82 cm

What does this residual plot suggest?

• The data is linear

• The data is non-linear

• The data has a smiley face

• The data has a negative trend

Which transformation could be used to linearise the data?

• $y^2$

• $x^2$

• log y

• $\frac{1}{y}$

Which transformation should be applied to linear this data?

• $y^2$

• $\frac{1}{x}$

• Log x

• Log y

Which transformation could be used to linearise the data?

• Log x

• $x^2$

• $y^2$