# Correlation & Regression

Module 6: Correlation and Regression

A For the supermodel dataset at the right, treat height as the explanatory variable and weight as the response variable. (Data set is given in the excel file)

1 Is there a significant correlation? Show the null hypothesis, df and the test you used.

yes/no

null hypothesis

df

test

2 If the correlation is significant:

a slope

intercept

line equation

b What proportion of the variation in y is explained by variation in x?

c What is the appropriate hypothesis to test the slope?

d What is the confidence interval for the slope?

e What can you conclude about the slope?

f What is the predicted value (yhat) when x=69?

B For the female dataset at the right, treat weight (WT) as the explanatory variable and body mass index (BMI) as the response variable. (Data set is given in the excel file)

1 Is there a significant correlation? Show the null hypothesis, df and the test you used.

yes/no

null hypothesis

df

test

2 If the correlation is significant:

a slope

intercept

line equation

b What proportion of the variation in y is explained by variation in x?

c What is the appropriate hypothesis to test the slope?

d What is the confidence interval for the slope?

e What can you conclude about the slope?

f What is the predicted value (yhat) when x=120?

g What is the confidence interval for a mean response of y when x=120?

C For the male dataset at the right, treat weight (WT) as the explanatory variable and body mass index (BMI) as the response variable. (Data set is given in the excel file)

1 Is there a significant correlation? Show the null hypothesis, df and the test you used.

yes/no

null hypothesis

df

test

2 If the correlation is significant:

a slope

intercept

line equation

b What proportion of the variation in y is explained by variation in x?

c What is the appropriate hypothesis to test the slope?

d What is the confidence interval for the slope?

e What can you conclude about the slope?

f What is the predicted value (yhat) when x=180?

g What is the prediction interval for an individual y value when x=180?

D For the male dataset at the right, treat weight (WT) as the explanatory variable and cholesterol (CHOL) as the response variable.

1 Is there a significant correlation? Show the null hypothesis, df and the test you used.

yes/no

null hypothesis

df

test

a slope

intercept

line equation

b What proportion of the variation in y is explained by variation in x?

c What is the appropriate hypothesis to test the slope?

d What is the confidence interval for the slope?

e What can you conclude about the slope?

f What is the predicted value (yhat) when x=200?

g What is the confidence interval for a mean response of y when x=200?

See attached file for problems.

#### Solution Summary

The solution provides step by step method for the calculation of correlation coefficient, test statistic for significance of correlation coefficient and regression analysis. Formula for the calculation and Interpretations of the results are also included.