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WorksheetsData Linear Association
Total questions: 25
Worksheet time: 53mins
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?
(a)
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.):
(a)
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.):
(a)
The number of students (s) and the number of computers (c) in four secondary schools in Queensland are shown in the table below.
Knowing the least squares regression line us c = 0.8s+27.13, predict the number of computers at James Nash SHS (s = 1400)
(a)
The number of students (s) and the number of computers (c) in four secondary schools in Queensland are shown in the table below.
Knowing the least squares regression line us c = 0.8s+27.13, James Nash has 300 computers. How many students should this service?
(a)
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 = 2.3x + 31.4, where x is the number of hours spent fishing, and y is the total number of fish caught.
Use the model to predict the number of fish caught if 12 hours were spent fishing.
(a)
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 = 2.3x + 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 positive association
moderate negative association
moderate strong association
moderate strong positive association
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 = 2.3x + 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.
There is a moderate relationship, so therefore it must have a linear relationship.
47% of the variation in fishing results can be explained by the variation of hours.
The following data for the height of five seedlings was collected and the least-squares line was developed and graphed.
Use the least-squares line to estimate the height of a nine-day-old seedling.
(a)
The following data for the height of five seedlings was collected and the least-squares line was developed and graphed.
When predicting the height of a 9 day old seedling, is this interpolating or extrapolating?
Interpolating
Extrapolating
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.
Extrapolating is inaccurate.
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.
Positive linear relationship
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. Identify the number of meals sold in that month
(a)
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 r2 value a little.
Decrease the r2 value a lot; otherwise it would be perfect 1.
Increase the r2 value a lot; otherwise it would be perfect -1.
Increase the r2 value a little.
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. Use the line of best fit to predict the number of meals that will be sold in the 18th month of the business operation.
(a)
(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.
Calculate Pearson’s correlation coefficient (2 d.p.).
(a)
(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 appropriate as the data has a linear form.
A linear model is not appropriate as the data has a nonlinear form.
(P2) The least-squares line for a sample of five data points was found to be y = 2.1875x + 0.0625, with a correlation coefficient of r = 0.875.
Determine a set of values for p and q, given that these values differ by 3. Enter the value of p:
(a)
P2 A teacher wants to know the best way for their students to improve their marks. They surveyed a sample of students who graduated last year and found the following data.
Which explanatory variable is the better predictor for the overall mark?
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