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Stat Tutor

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0:34

Correct. This is a correct statement.

Incorrect. This is a correct statement.

2

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Correct. The sign of correlation tells us direction and where it is on a scale from zero to one tells us the strength of the relationship.

Incorrect. The sign of correlation tells us direction and where it is on a scale from zero to one tells us the strength of the relationship.

2

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Correct. Regression gives us a formula for the line: \(\widehat{y} = a + bx\).

Incorrect. Regression gives us a formula for the line: \(\widehat{y} = a + bx\).

2

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1:33

Correct. X and Y can be interchanged in correlation, but not in the formula for a regression line: \(\widehat{y} = a + bx\).

Incorrect. X and Y can be interchanged in correlation, but not in the formula for a regression line:\(\widehat{y} = a + bx\).

2

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Correct. X and Y can be interchanged in correlation, but not in the formula for a regression line: \(\widehat{y} = a + bx\).

Incorrect. X and Y can be interchanged in correlation, but not in the formula for a regression line: \(\widehat{y} = a + bx\).

2

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Correct. X and Y can be interchanged in correlation, but not in the formula for a regression line: \(\widehat{y} = a + bx\).

Incorrect. X and Y can be interchanged in correlation, but not in the formula for a regression line: \(\widehat{y} = a + bx\).

2

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2:53

Correct. This is a correct statement.

Incorrect. This is a correct statement.

2

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Correct. This is a correct statement.

Incorrect. This is a correct statement.

2

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Correct. This is a correct statement.

Incorrect. This is a correct statement.

2

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Correct. If correlation, r, is negative, then slope will always be negative.

Incorrect. If correlation, r, is negative, then slope will always be negative.

2

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Correct. Knowing the value of slope only tells us the direction of r; the value of slope tells us nothing about the value of r.

Incorrect. Knowing the value of slope only tells us the direction of r; the value of slope tells us nothing about the value of r.

2

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3:18

Correct. This is a correct statement.

Incorrect. This is a correct statement.

2

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7:07

Correct. When all of the data points are on the regression line, r is either –1.0 or +1.0. So, r^{2} will be 100%.

Incorrect. When all of the data points are on the regression line, r is either –1.0 or +1.0. So, r^{2} will be 100%.

2

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Correct. When there is no relationship between X and Y, the cloud of data should resemble a hamburger bun.

Incorrect. When there is no relationship between X and Y, the cloud of data should resemble a hamburger bun.

2

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Correct. We expect the data points to be close to the regression line when r^{2} is close to 100% and scattered when r^{2} is close to 0%.

Incorrect. We expect the data points to be close to the regression line when r^{2} is close to 100% and scattered when r^{2} is close to 0%.

2

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Correct. In statistics we are very concerned about variation and r^{2} tells us about the variation in y.

Incorrect. In statistics we are very concerned about variation and r^{2} tells us about the variation in y.

2

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8:22

Correct. This is a correct statement.

Incorrect. This is a correct statement.

2

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9:53

Correct. This is a correct statement.

Incorrect. This is a correct statement.

2

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Correct. If r^{2} is really close to 100%, then there is very little unexplained variation.

Incorrect. If r^{2} is really close to 100%, then there is very little unexplained variation.

2

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10:31

Correct. r^{2} is a measure of the fraction of *variation in the y’s* that is explained by x. It does not tell us the fraction of y values that are exactly predicted as most are not, even when r^{2} is close to 100%.

Incorrect. r^{2} is a measure of the fraction of *variation in the y’s* that is explained by x. It does not tell us the fraction of y values that are exactly predicted as most are not, even when r^{2} is close to 100%.

2

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12:34

Correct. The variability of the y’s about their mean \( \overline{y} \) is called the total variation in y. The variability of the y’s about the regression line is a measure of the prediction errors (or residuals).

Incorrect. The variability of the y’s about their mean \( \overline{y} \) is called the total variation in y. The variability of the y’s about the regression line is a measure of the prediction errors (or residuals).

2

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Correct. If the prediction errors are small, then there is very little unexplained variation in the y’s and r^{2} is close to 100%. On the other hand, if the prediction errors are large, then there is a lot of unexplained variation and r^{2} is close to 0%.

Incorrect. If the prediction errors are small, then there is very little unexplained variation in the y’s and r^{2} is close to 100%. On the other hand, if the prediction errors are large, then there is a lot of unexplained variation and r^{2} is close to 0%.

2

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13:55

Correct. r^{2} tells us the percentage of variation in y that is explained by x. And the closer r^{2} is to 100%, the greater the variation in y that gets explained. So an r^{2} of 89% tells us that more variation in y is explained than when r^{2} is 47%.

Incorrect. r^{2} tells us the percentage of variation in y that is explained by x. And the closer r^{2} is to 100%, the greater the variation in y that gets explained. So an r^{2} of 89% tells us that more variation in y is explained than when r^{2} is 47%.

2

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Correct. r^{2} tells us the percentage of variation in y that is explained by x. So, r^{2} = (0.90)^{2} = 0.81 or 81% of the variation in blood alcohol content can be explained by number of beers consumed.

Incorrect. r^{2} tells us the percentage of variation in y that is explained by x. So, r^{2} = (0.90)^{2} = 0.81 or 81% of the variation in blood alcohol content can be explained by number of beers consumed.

2

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