Data was collected relating the number of hours spent fishing and the total number of fish caught. The linear model for this data was found to be y = 2.3 x + 31.4, where x is the number of hours spent fishing, and y is the total number of fish caught. The correlation coefficient for this data is 0.688. This means:

moderate strong positive association

Data was collected relating the number of hours spent fishing and the total number of fish caught. The linear model for this data was found to be y = 2.3 x + 31.4, where x is the number of hours spent fishing, and y is the total number of fish caught. The correlation coefficient for this data is 0.688. To describe this in terms of the variables and it's reasonableness....

For every hour spent fishing, the number of fish caught increases by 2.3.

Theoretically, if you spent no time fishing, you would catch 31.4 fish.

Confounding factors likely come into play, or the weak correlation may be caused by a nonlinear relationship.

47% of the variation in fishing results can be explained by the variation of hours.

There is a moderate relationship, so therefore it must have a linear relationship.

The following data for the height of five seedlings was collected and the least-squares line was developed and graphed. Based on the graph, the following statement was made: ‘A seedling will reach a height of about 32 cm by day 29.’ Pick comments on the reasonableness of this statement.

The data trend is flattening at 25cm, so predicting a higher value is inaccurate.

That follows the trendline, and there is a large quantity of data which was used for the trendline so it is probably accurate.

The number of meals sold (𝑦) by a restaurant each month (𝑥) for the first six months of business is shown on the scatterplot below. The line of best fit, its equation and the coefficient of determination (r²) are also shown. The restaurant was closed for renovations for most of one month. Describe the effect that this outlier has on the coefficient of determination.

Decrease the r 2 value a lot; otherwise it would be perfect 1.

Decrease the r 2 value a little.

Increase the r 2 value a lot; otherwise it would be perfect -1.

Increase the r 2 value a little.

(P2) The number of people living in each household and the average daily household water usage, measured in litres (L), were recorded for 10 households. Graph the data, and evaluate the appropriateness of using r=0.89 for the association between daily water usage and the number of people living in a household.

A linear model is not appropriate as the data has a nonlinear form.

A linear model is appropriate as the data has a linear form.

Linear Relationship and Bivariate Data

Authored by Barbara White

Mathematics

11th Grade - University

CCSS covered

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MULTIPLE CHOICE QUESTION

1 min • 1 pt

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.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

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

MULTIPLE CHOICE QUESTION

1 min • 1 pt

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.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

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.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

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?

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

MULTIPLE CHOICE QUESTION

1 min • 1 pt

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

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Linear Relationship and Bivariate Data

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

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

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?

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

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?

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

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

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.):

Access all questions and much more by creating a free account

Similar Resources on Wayground

Popular Resources on Wayground

Discover more resources for Mathematics

Linear Relationship and Bivariate Data

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

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

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?

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

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?

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

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

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.):

Access all questions and much more by creating a free account

Similar Resources on Wayground

Popular Resources on Wayground

Discover more resources for Mathematics

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.):