Question 3 uq for regression prediction cg q3a create an...

# QUESTION 3 --- UQ for regression prediction # CG Q3a # Create an object called nd that is the 1st row ########## in the ames data frame. nd <- ames[1, ] # CG Q3b # Use the predict() function to make a prediction ########## of log sales price and get the standard errors ########## for the first home in the ames data frame. ########## Name this object pred. pred <- predict(fit, newdata = nd, se.fit = TRUE) # CG Q3c # Use pred and a 1.96 critical value to ########## compute a 95% CI for the predicted log sales price ########## for the first home in the ames data frame. # CG Q3d # Wrap the line of code from Q3c in the exp() function ########## to get a 95% CI for the predicted sales price.

Transcript

00:02 Part 1.

00:04 This is the estimation result.

00:07 You have 3 explanatory variable, lot size, square feet and number of bedrooms.

00:16 So the numbers in blue are the estimated coefficient.

00:21 The numbers in green are the standard errors.

00:25 The r square of this regression is .672 and the number of observations is now we can calculate the predicted price for a house with a lot size of 10 ,000, the square feet of 2 ,300, and the number of bedroom of 4.

00:55 You can just plug these numbers into the equation and you will add the intercept.

01:03 Then you will get the predicted price as $336 ,714.

01:20 That is part 1 and for part 2.

01:27 You will regress price variable on lot size minus 10 ,000 and square feet minus 2 ,000 and 300 and bedrooms number of bedroom minus 4 we want the intercept estimate and the associated 95 % confidence interval from this regression recall that their confidence interval formula 95 % confidence interval is beta hat, the estimated coefficient, plus or minus the standard error of beta hat, times the value of the t statistic with at the alpha level of 5 % divided by 2, which is 0 .0 to 5 .5.

03:08 And the degrees of freedom is n number of observations in the regression minus k the number of coefficients then plus one so you will get the 95 % confidence confidence interval as 336707 plus minus 14 ,665.

04:01 So this is approximately 3 to 2 ,002, which is the lower bound of the confidence interval.

04:19 The upper bound is 351 ,372 and 372.

04:32 This is what you get when you round to the nearest dollar.

04:46 Part 3.

04:47 We will calculate the prediction interval.

04:56 So the formula for the prediction interval is y -had -nod - not, or y -not -had, which is the predicted value of the dependent variable, and in this case is the house price.

05:15 Plus or minus t statistic.

05:21 We want to obtain the 95 % confidence interval.

05:25 The 95 % confidence level is associated with an alpha level of 5%.

05:35 And this is a two -sided interval.

05:39 So we will use half of the alpha level, which is 0 .0 .05.

05:47 Okay, and we will find this t statistic for the degree of freedom as i wrote before in part two.

06:05 We will take this t statistic multiply with the standard error of e not hat.

06:15 And e not hat here is the prediction error...