Q: A frequency table for the number of live multiple-delivery births in California in 2012 is given. If the mean number of births is estimated as $$47.8$$ and the standard deviation as $$8.30$$, what is the coefficient of variation (CV)?

$$CV = \frac{8.30}{47.8} \times 100\% = 17.36\%$$

Q: If the regression equation is $$y = -0.5086x + 144.93$$, what is the residual for a winner who weighed $$110$$ pounds and for whom the actual number of winners was $$90$$?

Residual $$= 90 - (-0.5086 \times 110 + 144.93) = 90 - 89.98 = 0.02$$

Question 1

Given the following regression equation for predicting the number of Miss America winners from the weight in pounds: $$y = -0.5086x + 144.93$$, what is the predicted number of winners if the average winner's weight is 120 pounds?

Accepted Answer

$$y = -0.5086(120) + 144.93 = 83.90$$

Question 2

If the correlation coefficient $$r$$ between the weight of Miss America winners and the number of winners per year is $$-0.576$$, what does this value indicate?

Accepted Answer

There is a moderate negative linear relationship between weight and number of winners per year.

Question 3

Suppose you want to test if the correlation between weight and number of Miss America winners per year is statistically significant at $$\alpha = 0.05. $$Which of the following is the correct null hypothesis?

Accepted Answer

$$H_0$$: \rho = 0$$

Question 4

Given the regression equation $$y = -0.5086x + 144.93$$, what is the interpretation of the slope in the context of the Miss America data?

Accepted Answer

For each additional pound in weight, the predicted number of Miss America winners per year decreases by about 0.51.

Question 5

A student calculates the mean weight of Miss America winners as $$110.5$$ pounds and the standard deviation as $$9.41$$ pounds. If a winner weighed $$130$$ pounds, what is her $$z-$$score?

Accepted Answer

$$z = \frac{130 - 110.5}{9.41} = 2.07$$

Question 6

Which of the following best describes the meaning of the $$y-$$intercept in the regression equation $$y = -0.5086x + 144.93$$ for the Miss America data?

Accepted Answer

It is the predicted number of Miss America winners per year when the winner's weight is 0 pounds.

Question 7

A frequency table for the number of live multiple-delivery births in California in 2012 is given. If the mean number of births is estimated as $$47.8$$ and the standard deviation as $$8.30$$, what is the coefficient of variation (CV)?

Accepted Answer

$$CV = \frac{8.30}{47.8} 	imes 100\% = 17.36\%$$

Question 8

If the regression equation is $$y = -0.5086x + 144.93$$, what is the residual for a winner who weighed $$110$$ pounds and for whom the actual number of winners was $$90$$?

Accepted Answer

Residual $$= 90 - (-0.5086 	imes 110 + 144.93) = 90 - 89.98 = 0.02$$

Question 9

Which of the following statements about the correlation coefficient $$r is $$TRUE?

Accepted Answer

$$r$$ measures the strength and direction of a linear relationship between two quantitative variables.

Question 10

A student uses the regression equation $$y = -0.5086x + 144.93 to $$predict the number of Miss America winners for a weight of $$200$$ pounds. What is a potential problem with this prediction?

Accepted Answer

It is an extrapolation far outside the range of observed data, so the prediction may not be valid.

Question 11

Given a grouped frequency distribution, which formula is used to estimate the mean?

Accepted Answer

$$\bar{x} = \frac{\sum f_i m_i}{\sum f_i}$$, where $$f_i is $$the frequency and $$m_i is $$the class midpoint.

Question 12

If the standard deviation of a data set is $$s = 8.30$$ and the mean is $$\bar{x} = 47.8$$, what is the $$z-$$score for a value of $$60$$?

Accepted Answer

$$z = \frac{60 - 47.8}{8.30} = 1.47$$

Question 13

Which of the following is NOT an assumption for using linear regression analysis?

Accepted Answer

The relationship between the variables is nonlinear.

Question 14

If a frequency table has class midpoints $$m_i$$ and frequencies $$f_i$$, which formula estimates the population standard deviation $$\sigma$$?

Accepted Answer

$$\sigma = \sqrt{\frac{\sum f_i (m_i - \bar{x})^2$}{N}}$$

Question 15

A student claims that a correlation coefficient of $$r = -0.576$$ means that as one variable increases, the other always decreases. Is this correct?

Accepted Answer

No, it means there is a tendency for one variable to decrease as the other increases, but not always.

Question 16

Which of the following best describes the effect of an outlier on the correlation coefficient?

Accepted Answer

An outlier can greatly increase or decrease the value of $$r$$, potentially misleading the interpretation.

Question 17

If the sum of squared deviations for a grouped frequency distribution is $$656.56$$ and the total number of data values is $$6$$, what is the estimated population standard deviation?

Accepted Answer

$$\sigma = \sqrt{\frac{656.56}{6}} = 10.46$$

Question 18

Which of the following is the best reason to use a scatterplot before calculating the correlation coefficient?

Accepted Answer

To visually assess whether the relationship between the variables is linear.

Regression, Correlation, and Descriptive Statistics Study Guide

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