Week 7 HW

7.6 (a)

There is a strong positive correlation between husbands’ and wives’ ages as demonstrated by the upward and right direction of the data.

(b)

There does not appear to be a strong relationship between husbands’ and wives’s heights as the data are very spread out.

(c)

The age plot shows a stronger correlation because you could more accurately fit a line in the data.

(d)

The conversion from centimeters to inches does not impact the correlation because both variables (the husband and wife height) were converting using the same metric, so the relationship remains the same.

7.12 (a)

There is a slight positive relationship between volume and height. There is a wide spread of outcomes, especially as height increases, so it is not a very strong relationship.

(b)

There is a relatively strong positive relationship between volume and diameter. The residuals along a best fit line would be relatively small.

(c)

Diameter would be preferrable to use to predict volume because of the much stronger linear relationship described in part b as compared to part c.

7.18 (a)

The linear equation would be salary man = salary women + 5,000. The slope is positive so we’d have a positive correlation.

(b)

The linear equation would be salary man = salary women x 1.25. The slope is positive so we’d have a positive correlation.

(c)

The linear equation would be salary man = salary women x 0.85. The slope is positive so we’d have a positive correlation.

7.24 (a)

The number of calories and amount of carbohydrates have a moderate positive relationship as noted by the right upward sloping line. Many of the data points are away from the line, which is why it is only a moderate relationship.

(b)

The explanatory variable is the number of calories and the response variable is the number of carbohydrates.

(c)

A regression line would allow us to estimate the number of carbs in a food based on the number of calories listed. This information would be helpful for someone on a low carb diet.

(d)

The data show a linear trend. However, the the variability of points around the line is has a wide spread and the residuals are normally distributed, so it seems like the conditions are not satisfied.

7.30 (a)

Heart weight = -0.357 + 4.034 * body weight

(b)

It would be impossible for the cat to have 0 kg body weight so the intercept is not a meaningful number.

(c)

The slope says that we should expect every kg of body weight to add 4 g to the heart weight.

(d)

The R-squared says that 64.66% of the model’s variation in heart weight is explained by body weight.

(e)

The correlation coefficient is the square root of the R-squared:

sqrt(0.6466)

## [1] 0.8041144

7.36 (a)

There is a strong positive relationship between the number of cans of beer and the BAC.

(b)

BAC = -0.0127 + 0.018 * cans of beer

The slope says that we should expect every can of beer to add 0.018 grams per deciliter to your BAC. The intercept implies that you’d have a negative BAC is you had no beer, which doesn’t seem correct.

(c)

H0: B1 = 0. The true linear model has slope zero.

HA: B1 > 0. The true linear model has a slope greaters than zero. The more cans of beer consumed, the higher a person’s BAC.

The p-value is 0.0000 so we reject the null hypothesis. The data provide strong evidence that drinking more cans of beer is associated with an increase in blood alcohol.

(d)

The R-squared is:

0.89^2

## [1] 0.7921

79.21% of the variability in the model is explained by the number of cans of beer consumed.

(e)

No, I do not think the relationship would be as strong in a bar as in the study. The study was evenly distributed among men and women with different weights and drinking habits. People in a bar are unlikely to be as evenly distributed. In addition, they may not be independent if you select a group of people that has similar demographics and drinking habits.

7.42 (a)

The predicted head circumference for a baby whose gestational age is 28 weeks:

3.91 + 0.78*28

## [1] 25.75

(b)

H0: B1 = 0. The true linear model has slope zero.

HA: B1 > 0. The true linear model has a slope greaters than zero. The longer the gestational age, the larged the head circumference.

The p-value is between 0.001 and 0.025 so we reject the null hypothesis. The data provide strong evidence that a longer gestational age is associated with an increase in head circumference.

Week 7 HW

Greg Adelsberger

3/2/2018

7.6

(a)

There is a strong positive correlation between husbands’ and wives’ ages as demonstrated by the upward and right direction of the data.

(b)

There does not appear to be a strong relationship between husbands’ and wives’s heights as the data are very spread out.

(c)

The age plot shows a stronger correlation because you could more accurately fit a line in the data.

(d)

The conversion from centimeters to inches does not impact the correlation because both variables (the husband and wife height) were converting using the same metric, so the relationship remains the same.

7.12

(a)

There is a slight positive relationship between volume and height. There is a wide spread of outcomes, especially as height increases, so it is not a very strong relationship.

(b)

There is a relatively strong positive relationship between volume and diameter. The residuals along a best fit line would be relatively small.

(c)

Diameter would be preferrable to use to predict volume because of the much stronger linear relationship described in part b as compared to part c.

7.18

(a)

The linear equation would be salary man = salary women + 5,000. The slope is positive so we’d have a positive correlation.

(b)

The linear equation would be salary man = salary women x 1.25. The slope is positive so we’d have a positive correlation.

(c)

The linear equation would be salary man = salary women x 0.85. The slope is positive so we’d have a positive correlation.

7.24

(a)

The number of calories and amount of carbohydrates have a moderate positive relationship as noted by the right upward sloping line. Many of the data points are away from the line, which is why it is only a moderate relationship.

(b)

The explanatory variable is the number of calories and the response variable is the number of carbohydrates.

(c)

A regression line would allow us to estimate the number of carbs in a food based on the number of calories listed. This information would be helpful for someone on a low carb diet.

(d)

The data show a linear trend. However, the the variability of points around the line is has a wide spread and the residuals are normally distributed, so it seems like the conditions are not satisfied.

7.30

(a)

Heart weight = -0.357 + 4.034 * body weight

(b)

It would be impossible for the cat to have 0 kg body weight so the intercept is not a meaningful number.

(c)

The slope says that we should expect every kg of body weight to add 4 g to the heart weight.

(d)

The R-squared says that 64.66% of the model’s variation in heart weight is explained by body weight.

(e)

The correlation coefficient is the square root of the R-squared:

7.36

(a)

There is a strong positive relationship between the number of cans of beer and the BAC.

(b)

BAC = -0.0127 + 0.018 * cans of beer

The slope says that we should expect every can of beer to add 0.018 grams per deciliter to your BAC. The intercept implies that you’d have a negative BAC is you had no beer, which doesn’t seem correct.

(c)

H0: B1 = 0. The true linear model has slope zero.

HA: B1 > 0. The true linear model has a slope greaters than zero. The more cans of beer consumed, the higher a person’s BAC.

The p-value is 0.0000 so we reject the null hypothesis. The data provide strong evidence that drinking more cans of beer is associated with an increase in blood alcohol.

(d)

The R-squared is:

79.21% of the variability in the model is explained by the number of cans of beer consumed.

(e)

7.42

(a)

The predicted head circumference for a baby whose gestational age is 28 weeks:

(b)

H0: B1 = 0. The true linear model has slope zero.

HA: B1 > 0. The true linear model has a slope greaters than zero. The longer the gestational age, the larged the head circumference.

The p-value is between 0.001 and 0.025 so we reject the null hypothesis. The data provide strong evidence that a longer gestational age is associated with an increase in head circumference.