Home work 1: Stat 530 Due Feb Jan 22: (20 points)
1. Write TRUE or FALSE with reasons for the following:
a.
b.
c.
d.
Hair color is a categorical random variable.
Normal distribution is symmetric, t, chi-square and F are skewed.
If y follows normal with mean 2 and variance 1, y^2 follows a chi-square distribution with 1 df.
If y1 is a normal with mean 0 and variance 1, and y2 follows chi-square with n-1 degrees of
freedom then y1/sqrt(y2/n-1) follows a t distribution with (n-1) degrees of freedom
e. If y3 follows a t distribution then y3^2 follows F.
2. Consider the data set on age and cholesterol given in our class website names Hw1-2015.xls.
Answer the questions based on this data set:
a. Why is Cholesterol considered the response variable? Why is age the explanatory variable?
b. Plot the relationship. What do you see from the plot?
c. Determine least squares’ equation that can be used for predicting Cholesterol.
3. Why is the regression estimates called the LEAST SQUARE estimates. Comment.
4. Give an example from your discipline where you think linear regression would be appropriate.