The number of bees leaving a hive was observed and recorded over 14 days at different times of the day.
Which Pearson's correlation coefficient best describes the observations?
Statistics, STD2 S4 2021 HSC 28
A salesperson is interested in the relationship between the number of bottles of lemonade sold per day and the number of hours of sunshine on the day.
The diagram shows the dataset used in the investigation and the least-squares regression line.
- Find the equation of the least-squares regression line relating to the dataset. (2 marks)
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- Suppose a sixth data point was collected on a day which had 10 hours of sunshine. On that day 45 bottles of lemonade were sold.
- What would happen to the gradient found in part (a)? (1 mark)
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Statistics, STD2 S4 EQ-Bank 4
Ten high school students have their height and the length of their right foot measured.
The results are recorded in the table below.
- Using technology, calculate Pearson's correlation coefficient for the data. Give your answer to 3 decimal places. (1 mark)
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- Describe the strength of the association between height and length of right foot for these students. (1 mark)
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- Using technology, determine the least squares regression line that allows height to be predicted from right foot length. (1 mark)
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Statistics, 2ADV S2 EQ-Bank 3
The table below lists the average life span (in years) and average sleeping time (in hours/day) of 9 animal species.
- Using sleeping time as the independent variable, calculate the least squares regression line. (1 mark)
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- A wallaby species sleeps for 4.5 hours, on average, each day.
Use your equation from part i to predict its expected life span, to the nearest year. (1 mark)
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Statistics, 2ADV S2 EQ-Bank 2
The table below lists the average body weight (in kilograms) and average brain weight (in grams) of nine animal species.
A least squares regression line is fitted to the data using body weight as the independent variable.
- Calculate the equation of the least squares regression line. (1 mark)
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- If dingos have an average body weight of 22.3 kilograms, calculate the predicted average brain weight of a dingo using your answer to part i. (1 mark)
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Statistics, 2ADV S2 EQ-Bank 1
The arm spans (in cm) and heights (in cm) for a group of 13 boys have been measured. The results are displayed in the table below.
The aim is to find a linear equation that allows arm span to be predicted from height.
- What will be the independent variable in the equation? (1 mark)
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- Assuming a linear association, determine the equation of the least squares regression line that enables arm span to be predicted from height. Write this equation in terms of the variables arm span and height. Give the coefficients correct to two decimal places. (2 marks)
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- Using the equation that you have determined in part b., interpret the slope of the least squares regression line in terms of the variables height and arm span. (1 mark)
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Statistics, STD2 S4 2019 HSC 23
A set of bivariate data is collected by measuring the height and arm span of seven children. The graph shows a scatterplot of these measurements.
- Calculate Pearson's correlation coefficient for the data, correct to two decimal places. (1 mark)
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- Identify the direction and the strength of the linear association between height and arm span. (1 mark)
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- The equation of the least-squares regression line is shown.
Height = 0.866 × (arm span) + 23.7
A child has an arm span of 143 cm.
Calculate the predicted height for this child using the equation of the least-squares regression line. (1 mark)
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