Linear Relationship and Bivariate Data

Question 1. Two variables are displayed on a scatterplot. Which statement below is correct?

• Only if there is a causal relationship between the two variables will they have a positive association.

• If the two variables have a negative association then there is not a causal relationship between the two variables.

• If the two variables are associated either positively or negatively then there could be a causal relationship between the two variables.

• If the two variables are associated either positively or negatively then there is definitely a causal relationship between the two variables.

The following scatterplot shows a linear association between two numerical variables. Choose the best description for the direction and strength of the association.

• strong positive

• strong negative

• weak positive

• weak negative

It is observed that as the number of ice blocks sold each month increases, the number of fans sold also increases. Which of these statements is therefore true?

• There is a negative causation between the number of ice blocks sold and the number of fans sold each month.

• There is a positive causation between the number of ice blocks sold and the number of fans sold each month.

• There is a negative association between the number of ice blocks sold and the number of fans sold each month.

• There is a positive association between the number of ice blocks sold and the number of fans sold each month.

Fitting a least-squares line to create a model from a set of time series data ensures that

• the distances between the data points and the line of best fit are minimised.

• the same number of data points are above and below the line of best fit.

• the distances between the data points and the axes are minimised.

• the least-squares distances of all data points are added together.

Question 1. Some students had their height and foot lengths measured and recorded. The results were graphed and a line of best fit was drawn by four different students as shown. Which of the following shows the most suitable line of best fit?

• A

• B

• C

• D

Four linear models have been developed for a data set. Identify the residual plot that indicates that the developed linear model is justified

• A

• B

• C

• D

Determine the equation of the least-squares line where the information in the image is true.

• y = 16.8x - 1147

• y = 16.8x - 19

• y = 0.05x + 68.33

• y = 0.05x + 1.7

The number of students (s) and the number of computers (c) in four secondary schools in Queensland are shown in the table below. What is the response variable?

The number of students (s) and the number of computers (c) in four secondary schools in Queensland are shown in the table below.

Determine a linear relationship for this data by fitting a least-squares line to the data. Enter in the slope (2 d.p.):

The number of students (s) and the number of computers (c) in four secondary schools in Queensland are shown in the table below.

Determine a linear relationship for this data by fitting a least-squares line to the data. Enter in the y-intercept (2 d.p.):