Correlation & Causality

Statistics

AP Statistics

IB Mathematics

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| By Anthony Nunan

Anthony Nunan

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Quizzes Created: 132 | Total Attempts: 47,826

| Attempts: 332 | Questions: 15

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Question 1 / 15

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1) Mr Magoo is trying to demonstrate how important it is for his students to get a good grounding in Chapter 1 in order to continue with Chapter 2. He has mapped the marks of the first test to the x variable, and the second test to the y variable. The results are plotted below.

According to the line of linear regression, he has a Coefficient of Determination of 0.6447 Which statement is most correct :

80% of the variation in the Chapter 2 test results and be explained by the variation in the Chapter 1... 80% of the variation in the Chapter 2 test results and be explained by the variation in the Chapter 1 test results.

80% of the variation in his Chapter 1 test results can be explained by the variation in the Chapter 2... 80% of the variation in his Chapter 1 test results can be explained by the variation in the Chapter 2 test results.

64% of the variation in the Chapter 2 test results and be explained by the variation in the Chapter 1... 64% of the variation in the Chapter 2 test results and be explained by the variation in the Chapter 1 test results.

64% of the variation in his Chapter 1 test results can be explained by the variation in the Chapter 2... 64% of the variation in his Chapter 1 test results can be explained by the variation in the Chapter 2 test results.

The relationship between the two variables is non-linear

The correct answer is "64% of the variation in the Chapter 2 test results can be explained by the variation in the Chapter 1 test results." This means that the linear regression line can account for 64% of the variability in the Chapter 2 test scores based on the Chapter 1 test scores. It indicates that there is a moderate positive relationship between the two variables, where higher scores in Chapter 1 tend to be associated with higher scores in Chapter 2.

Explanation

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About This Quiz

The Coefficient of Determination is generally measured as a percentage. If it is 95% then the statement would read as :
95% of the variation of the dependent variable (y variable), can be explained by the variation in the independent variable (x variable)

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2) Jacob is on a fitness campaign. He is measuring his improvement by counting the number of pushups he can do in one minute. He measures his progress at the end of each week.

According to the line of linear regression, he has a Correlation Coefficient of 0.88 Which statement is most correct :

88% of the variation in his push up count can be explained by the number of weeks he has attended... 88% of the variation in his push up count can be explained by the number of weeks he has attended training

88% of the variation in his weekly attendance explained by the variation in his push-up count

78% of the variation in his push up count can be explained by the number of weeks he has attended... 78% of the variation in his push up count can be explained by the number of weeks he has attended training

78% of the variation in his weekly attendance explained by the variation in his push-up count

The relationship between attendance at training and pushups is non-linear

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Explanation

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3) Mr Magoo is trying to demonstrate how important it is for his students to get a good grounding in Chapter 1 in order to continue with Chapter 2. He has mapped the marks of the first test to the x variable, and the second test to the y variable. The results are plotted below.

According to the line of linear regression, he has an r value of 0.80 Which statement is most correct :

The relationship between the two variables is non-linear

The correct answer is "64% of the variation in the Chapter 2 test results can be explained by the variation in the Chapter 1 test results." This is because the r value of 0.80 indicates the strength and direction of the linear relationship between the two variables. In this case, it means that 64% of the variation in the Chapter 2 test results can be attributed to the variation in the Chapter 1 test results.

Explanation

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4) Jack is on a fitness campaign. He is measuring his improvement by counting the number of pushups he can do in one minute. He measures his progress at the end of each week.

According to the line of linear regression, he has an

of 0.89. Which statement is most correct :

94% of the variation in his push up count can be explained by the number of weeks he has attended... 94% of the variation in his push up count can be explained by the number of weeks he has attended training

94% of the variation in his weekly attendance explained by the variation in his push-up count

89% of the variation in his push up count can be explained by the number of weeks he has attended... 89% of the variation in his push up count can be explained by the number of weeks he has attended training

89% of the variation in his weekly attendance explained by the variation in his push-up count

There relationship between attendance and pushups is non-linear

The correct answer is "89% of the variation in his push up count can be explained by the number of weeks he has attended training." This means that 89% of the changes in Jack's push up count can be attributed to the number of weeks he has attended training. The line of linear regression suggests that there is a strong positive relationship between the number of weeks of training and the improvement in push up count.

Explanation

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5) The cardio section of a hospital is looking at a new medication to lower resting heart rates in patients. The medication starts to have an impact after 40 days. The x axis is the number of days the patient has been taking mediation, and the y axis is the resting heart rate.

According to the line of linear regression, the value of

is 0.85. Which statement is most correct :

85% of the variation resting heart rate can be explained by the variation in the number of days a patient... 85% of the variation resting heart rate can be explained by the variation in the number of days a patient has been on the medication.

85% of the variation in the number of days a patient has been on medication can be explained by the... 85% of the variation in the number of days a patient has been on medication can be explained by the variation in the resting heart rate.

92% of the variation resting heart rate can be explained by the variation in the number of days a patient... 92% of the variation resting heart rate can be explained by the variation in the number of days a patient has been on the medication.

92% of the variation in the number of days a patient has been on medication can be explained by the... 92% of the variation in the number of days a patient has been on medication can be explained by the variation in the resting heart rate.

The relationship between the two variables is non linear

85% of the variation in resting heart rate can be explained by the variation in the number of days a patient has been on the medication. This means that the number of days a patient has been on the medication is a strong predictor of their resting heart rate, accounting for 85% of the variability in heart rate. The remaining 15% of the variability is likely due to other factors that are not accounted for in the linear regression model.

Explanation

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6) The cardio section of a hospital is looking at a new medication to lower resting heart rates in patients. The medication starts to have an impact after 40 days. The x axis is the number of days the patient has been taking mediation, and the y axis is the resting heart rate.

According to the line of linear regression, the Coefficient of Determination is 0.85. Which statement is most correct :

The relationship between the two variables is non linear

85% of the variation resting heart rate can be explained by the variation in the number of days a patient has been on the medication. This means that the medication has a significant impact on lowering the resting heart rate, as 85% of the changes in heart rate can be attributed to the number of days the patient has been taking the medication.

Explanation

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7) Jack is on a fitness campaign.He is measuring his improvement by counting the number of pushups he can do in one minute.He measures his progress at the end of each week.

According to the line of linear regression, he has a Correlation Coefficient of 0.94.Which statement is most correct :

94% of the variation in his weekly attendance explained by the variation in his push-up count

89% of the variation in his weekly attendance explained by the variation in his push-up count

There relationship between attendance and pushups is non-linear

The correlation coefficient of 0.94 indicates a strong positive linear relationship between the number of weeks Jack has attended training and his push up count. However, the statement "94% of the variation in his push up count can be explained by the number of weeks he has attended training" is not correct. The correct statement is "89% of the variation in his push up count can be explained by the number of weeks he has attended training." This means that the number of weeks attended training explains 89% of the variability in Jack's push up count.

Explanation

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8) The cardio section of a hospital is looking at a new medication to lower resting heart rates in patients. The medication starts to have an impact after 40 days. The x axis is the number of days the patient has been taking mediation, and the y axis is the resting heart rate.

According to the line of linear regression, the r value is -0.924 Which statement is most correct :

The relationship between the two variables is non linear

The correct answer is "85% of the variation resting heart rate can be explained by the variation in the number of days a patient has been on the medication." This means that 85% of the changes or differences in resting heart rate can be attributed to the number of days a patient has been taking the medication. The higher the number of days on the medication, the greater the impact on lowering the resting heart rate. The linear regression line with an r value of -0.924 indicates a strong negative correlation between the number of days on medication and resting heart rate.

Explanation

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9) Jack is on a fitness campaign. He is measuring his improvement by counting the number of pushups he can do in one minute. He measures his progress at the end of each week.

According to the line of linear regression, he has Coefficient of Determintion of 0.89. Which statement is most correct :

94% of the variation in his weekly attendance explained by the variation in his push-up count

89% of the variation in his weekly attendance explained by the variation in his push-up count

There relationship between attendance and pushups is non-linear

The correct answer is "89% of the variation in his push up count can be explained by the number of weeks he has attended training". This means that the number of weeks Jack has attended training can account for 89% of the changes in his push up count. The coefficient of determination, also known as R-squared, measures the proportion of the dependent variable's variance that can be explained by the independent variable(s). In this case, the independent variable is the number of weeks attended training and the dependent variable is the push up count.

Explanation

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10) Mr Magoo is trying to demonstrate how important it is for his students to get a good grounding in Chapter 1 in order to continue with Chapter 2. He has mapped the marks of the first test to the x variable, and the second test to the y variable. The results are plotted below.

According to the line of linear regression, he has an

value of 0.6447 Which statement is most correct :

The relationship between the two variables is non-linear

The correct answer is "64% of the variation in the Chapter 2 test results can be explained by the variation in the Chapter 1 test results." This means that the x variable (Chapter 1 test results) can account for 64% of the variability in the y variable (Chapter 2 test results) based on the line of linear regression.

Explanation

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11) Paddy is on a fitness campaign. He is measuring his improvement by counting the number of pushups he can do in one minute. He measures his progress at the end of each week.

According to the line of linear regression, he has a Correlation Coefficient of 0.91 Which statement is most correct :

91% of the variation in his push up count can be explained by the number of weeks he has attended... 91% of the variation in his push up count can be explained by the number of weeks he has attended training

91% of the variation in his weekly attendance explained by the variation in his push-up count

82% of the variation in his push up count can be explained by the number of weeks he has attended... 82% of the variation in his push up count can be explained by the number of weeks he has attended training

82% of the variation in his weekly attendance explained by the variation in his push-up count

The relationship between attendance at training and pushups is non-linear

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Explanation

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12) Jack is on a fitness campaign. He is measuring his improvement by counting the number of pushups he can do in one minute. He measures his progress at the end of each week.

According to the line of linear regression, he has an 'r' value of 0.94. Which statement is most correct :

94% of the variation in his weekly attendance explained by the variation in his push-up count

89% of the variation in his weekly attendance explained by the variation in his push-up count

There relationship between attendance and pushups is non-linear

The correct answer is "89% of the variation in his push up count can be explained by the number of weeks he has attended training." This means that 89% of the changes or differences in Jack's push up count can be attributed to the number of weeks he has attended training. The remaining 11% of the variation may be due to other factors that are not accounted for in this analysis.

Explanation

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13) The cardio section of a hospital is looking at a new medication to lower resting heart rates in patients. The medication starts to have an impact after 40 days. The x axis is the number of days the patient has been taking mediation, and the y axis is the resting heart rate.

According to the line of linear regression, the Correlation Coefficient is -0.924 Which statement is most correct :

The relationship between the two variables is non linear

The correct answer is "85% of the variation resting heart rate can be explained by the variation in the number of days a patient has been on the medication." This is because the correlation coefficient of -0.924 indicates a strong negative linear relationship between the number of days on the medication and the resting heart rate. The closer the correlation coefficient is to -1 or 1, the stronger the relationship. In this case, -0.924 indicates that as the number of days on the medication increases, the resting heart rate decreases, and this relationship explains 85% of the variation in the resting heart rate.

Explanation

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14) Mr Magoo is trying to demonstrate how important it is for his students to get a good grounding in Chapter 1 in order to continue with Chapter 2. He has mapped the marks of the first test to the x variable, and the second test to the y variable. The results are plotted below.

According to the line of linear regression, he has a Correlation Coefficient of 0.80 Which statement is most correct :

The relationship between the two variables is non-linear

The correct answer is "64% of the variation in the Chapter 2 test results can be explained by the variation in the Chapter 1 test results." This means that the correlation coefficient of 0.80 indicates that 64% of the changes in the Chapter 2 test results can be attributed to the changes in the Chapter 1 test results. It suggests a moderate positive linear relationship between the two variables.

Explanation

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15) Andrew is an archer. He is trying to see if there is a relationship between the time he spends aiming at a target, and the number of times he successfully hits the bullseye. He has spent 5 session shooting arrows with different aim times between one and five seconds. He has plotted the aim time on the x axis, and the number of bulls eye shots on the y axis.

According to the line of linear regression, the value of r is 0.9876. Which statement is most correct :

99% of the variation in bulls eye results can be explained by the variation in the time spent aiming at... 99% of the variation in bulls eye results can be explained by the variation in the time spent aiming at the target.

99% of the variation in time spend aiming at the target can be explained by the variation in the the... 99% of the variation in time spend aiming at the target can be explained by the variation in the the bulls eye results.

99% of the variation in bulls eye results can be explained by the variation in the time spend aiming at... 99% of the variation in bulls eye results can be explained by the variation in the time spend aiming at the target.

97% of the variation in time spent aiming at the target can be explained by the variation in the the... 97% of the variation in time spent aiming at the target can be explained by the variation in the the bulls eye results.

The relationship between the two variables is non linear

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Explanation

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