Question 3. [3 pts] For each of the following questions, explain whether a confidence interval for a mean response or a prediction interval for a new observation is appropriate.

(a) The Tri-City Office Equipment Corporation sells an imported copier on a franchise basis and performs preventive maintenance and repair service on this copier. How long will the service time be on the next call in which six copiers are serviced?

(b) The director of admissions of a small college wants determine whether a student's grade point average (GPA) at the end of the freshman year can be predicted from the ACT test score. What is the average

freshman GPA for students whose ACT test score is 28?

(c) A substance used in biological and medical research is shipped by airfreight to users in cartons of 1,000 ampules. What is the number of broken ampules for the next shipment which entails two transfers?: Let y = w0 +w1x+, where is a normally distributed random error with mean 0 and variance .

Consider fitting a least squares regression model y^ = w^0x + w^1. In linear regression, why do we usually minimize square error ( sum (y - ^y)2) rather than l1-norm ( sum( | y-y^ | ))?

Denote the residuals as e = y - ^y. Are the residuals e and fitted values ^y correlated? Why or why not?

[Hint: Simple linear regression is a special case of multi-linear regression, thus conclusions on multi-linear regression could still be applied, such as ^ Y = HY , where H = X(XT *X)-1 * XT .]

: What is the major difference between a simple linear regression model and a multiple linear regression model?

Group of answer choices

In simple linear regression you can only have quantitative explanatory variables. In multiple linear regression you can have quantitative and categorical explanatory variables.

In simple linear regression you have many explanatory variables. In multiple linear regression you have only one explanatory variable.

In simple linear regression you have only one explanatory variable. In multiple linear regression you can have many explanatory variables.

Question 7 (10 pts). For the given data below, linear regression of Y on X is applied. All the necessary calculations are made and shown on the table below. a) Determine the regression coefficients and write the regression equation of Yon X, b) Find the coefficient of determination and comment on whether the obtained regression equation is good for predicting the response value Y. 1,10