Question: a). For a random sample of 263 professionals, the correlation between their age and their income was found to be 0.17. Test the null hypothesis that there is no linear relationship between these two variables against the alternative that there is a positive relationship?

b). A sample of 8 households was asked about the amount of time they spend connected to the internet cash month as well as their monthly income. The data are presented in the following table.

Income 65 77 42 36 34 38 58 43

Hours 66 48 28 37 33 29 48 35

Calculate the linear regression of hours on income. How many hours would we except a household with an annual income of $66,000 to spend on the Internet?

c). Consider a random sample of 25 observations of the two variables X and Y. The following information is available.

∑yi=57.2 ∑Xi=1253.4 ∑xi2= 73296.4 ∑xiyi= 3133.7

Calculate the equation of the regression line of Y on X

d). What factors would tend to reduce the variation of a prediction from a simple linear regression?