Suppose that a dependent variable y is related to an explanatory variable x through a linear regression model with β0 = 4.2, β1 = 1.7. and with normally distributed error terms with a zero mean and a standard deviation of σ = 3?
(a) What is the expected value of the dependent variable when x = 10.0?
(b) How much does the expected value of the dependent variable change when the explanatory variable increases by 3?
(c) What is the probability that the dependent variable is larger than 12.0 when x = 5?
(d) What is the probability that the dependent variable is smaller than 17.0 when x = 8?
(e) What is the probability that a dependent variable obtained at x = 6 is larger than a dependent variable obtained at x = 7?