QUESTION 1: Heritability How does a person's height relate to the height of their parents? The adult heights (inches) of 898 children from 197 families were collected. In addition, the investigators also gathered the heights of the mother and father from each family. The data are reported in the Heritability.csv dataset (see Data Repository). Using this data, answer the following questions. Under which of the following situations is simple linear regression NOT suitable?

Residuals or error of the regression are normally distributed
There is a linear relationship between the response and independent variable.
The response variable is continuous.
The response variable is categorical.
 
QUESTION 2. Calculate the correlation between a person's height and their father's height. Round your answer to three decimal places.

QUESTION 3. Which of the following best describes the nature of the correlation between height and father's height?.

No correlation
Non-linear
Positive
Negative

QUESTION 4. What was the correct Null hypothesis for the hypothesis test of the correlation between a person's height and their father's height?
H0: ρ = 1
H0: ρ ≠ 0
H0: ρ = -1
H0: ρ = 0

QUESTION 5. What was the correct Alternate hypothesis for the hypothesis test of the correlation between a person's height and their father's height?
HA: ρ = 1
HA: ρ ≠ 0
HA: ρ = 0
HA: ρ = -1

QUESTION 6. What was the p-value for the correlation between a person's height and their father's height? Round your answer to three decimal places. If the p-value was less than 0.001, round to 0.001.

QUESTION 7. Calculate the lower bound of the 95% CI for the correlation between a person's height and their father's height. Round your answer to three decimal places.

QUESTION 8. Calculate the upper bound of the 95% CI for the correlation between a person's height and their father's height. Round your answer to three decimal places.

QUESTION 9. Which of the following statements best describes the correlation between a person's height and their father's height?

The height of a father determines the height of a child.
There was a statistically significant positive correlation between a person's height and their father's height.
There was no relationship between a person's height and their father's height .
There was NO statistically significant correlation between a person's height and their father's height .

QUESTION 10. Perform a simple linear regression using father's height to predict a person's height. What was the r-square value of the regression model? Round your answer to three decimal places.

QUESTION 11. Which of the following statements best defines the r-square value?

A total of 7.6% of the variability in a father's height can be explained by a linear relationship with their child's height.
A total of 7.6% of the variability in a person's height can be explained by a linear relationship with their father's height.
A father's height determines 7.6% of the variability in their child's height.
A total of 73.51% of the variability in a person's height can be explained by a linear relationship with their father's height.

QUESTION 12. What was the value of the intercept for the linear regression predicting a person's height using their father's height? Round answer to three decimal places.

QUESTION 13. What was the value of the slope for the linear regression predicting a person's height using their father's height? Round your answer to three decimal places.

QUESTION 14. Which of the following statements best defines the slope for the linear regression predicting a person's height using their father's height?

The average person's height when a father's height was equal to 0 was 39.11.
The average person's height when a father's height was equal to 0 was 0.399.
For every one unit increase in father's height, a person's height decreased by 0.399.
For every one unit increase in father's height, a person's height increased by 0.399.

QUESTION 15. Which of the following was the correct Null hypothesis for the Hypothesis test of the slope?
H0: α = 0
H0: ε = 0
H0: β = 0
H0: β ≠ 0

QUESTION 16. What was the p-value for the hypothesis test of the slope? Round you answer to three decimal places. If the p-value was less than 0.001, round to 0.001.

QUESTION 17. What was the lower bound of the 95% CI of the father's height slope for the linear regression predicting a person's height? Round you answer to three decimal places.

QUESTION 18. What was the upper bound of the 95% CI of the father's height slope for the linear regression predicting a person's height? Round your answer to three decimal places.

QUESTION 19. What was the correct decision for the hypothesis test of the slope?
Reject H0
Fail to Reject H0
Accept H0
Accept HA

QUESTION 20. Which of the following statements best summarises the findings from the linear regression analysis?

There was a statistically significant positive linear relationship between a father's height and a person's height.
There was no association between between a father's height and a person's height.
The height of a father determines the height of their children.
There was NO statistically significant linear relationship between a father's height and a person's height.

QUESTION 21. Crawling

This study investigated whether babies take longer to learn to crawl in cold months when they are often bundled in clothes that restrict their movement, than in warmer months. The study sought an association between babies' first crawling age and the average temperature (Fahrenheit) during the month they first try to crawl (about 6 months after birth). Parents brought their babies into the University of Denver Infant Study Center between 1988-1991 for the study. The parents reported the birth month and age at which their child was first able to creep or crawl a distance of four feet in one minute. Data were collected on 208 boys and 206 girls (40 pairs of which were twins).The Crawling.csv dataset can be downloaded from the Data Repository. The file contains summary data including the number of infants born during each month, the mean and standard deviation of their crawling ages, and the average monthly temperature six months after the birth month. Using this data, you will determine if there is a linear relationship between temperature and crawling age. Which of the following variables will be considered to be the predictor?

Average temperature
Month of birth
Average crawling age
Season of birth

QUESTION 22. Calculate the correlation between temperature and average crawling age. Round your answer to three decimal places.

QUESTION 23. Describe the correlation between temperature and average crawling age.
Negative
Non-linear
No correlation
Positive

QUESTION 24. What is the p-value for the correlation between temperature and average crawling age? Round your answer to three decimal places. If the p-value is less than 0.001, round to 0.001.

QUESTION 25. Calculate the lower bound of the 95% CI for the correlation between temperature and average crawling age. Round you answer to three decimal places.

QUESTION 26. Calculate the upper bound of the 95% CI for the correlation between temperature and average crawling age. Round your answer to three decimal places.

QUESTION 27. Which of the following statements best describes the correlation between temperature and average crawling age?

There was no relationship between temperature and average crawling age.
There was NO statistically significant correlation between temperature and average crawling age.
Increased temperature cause significantly earlier average crawling ages.
There was a statistically significant negative correlation between temperature and average crawling age.

QUESTION 28. Perform a simple linear regression using temperature to predict average crawling age. What is the r-square value of the regression model? Round your answer to three decimal places.

QUESTION 29. What is the value of the constant for the linear regression predicting average crawling age using temperature? Round your answer to three decimal places.

QUESTION 30. Which of the following statements best defines the constant for the linear regression using temperature to predict average crawling age?

When temperature equals zero, the expected average crawling age will be 0.078.
For every one unit increase in temperature, the average crawling age decreases by -0.078.
For every one unit increase in temperature, the average crawling age increases by 35.678.
When temperature equals zero, the expected average crawling age will be 35.678.

QUESTION 31. What is the value of the slope for the linear regression predicting average crawling age using temperature? Round your answer to three decimal places.

QUESTION 32. Which of the following is the correct Alternate hypothesis for the Hypothesis test of the slope?

HA: β ≠ 0
HA: α = 0
HA: β = 0
HA: ε = 0

QUESTION 33. What is the value of the test statistic t for the hypothesis test of the slope? Round your answer to three decimal places.

QUESTION 34. What is the p-value for the hypothesis test of the slope? Round your answer to to three decimal places. If p-value is less than 0.001, round to 0.001.

QUESTION 35. What is the lower bound of the 95% CI of the temperature slope for the linear regression predicting average crawling age? Round your answer to three decimal places.

QUESTION 36. What is the upper bound of the 95% CI of the temperature slope for the linear regression predicting average crawling age? Round your answer to three decimal places.

QUESTION 37. What is the correct decision for the hypothesis test of the slope?

Reject H0
Fail to Reject H0
Accept H0
Accept HA

QUESTION 38. Which of the following statements best summarises the findings of the linear regression between temperature and average crawling age?

There was NO statistically significant linear relationship between temperature and average crawling age.
There was a statistically significant negative linear relationship between temperature and average crawling age.
There was a statistically significant positive linear relationship between temperature and average crawling age.
Increased temperatures cause significantly earlier average crawling ages.