Test 2 stats

95% CI for slope, B1

(B1) +/- (2)(stand error of B1)

What does the "constant variance" assumption for Simple Linear Regression actually mean?

The variation around the line is the same at each value of x

For a multiple linear regression model, the value of R^2 increases as the number of predictors/independent variables increases.

True

Interpret SD of MLR model

2 x standard deviation

Suppose (hypothetically) that we have conducted a Simple Linear Regression for Exam 1 score by Homework 1 score and found the predicted line equation to be y_hat = 58.25 + 2.25x, where x represents Homework 1 score and y represents Exam 1 score. What Exam 1 score can a student who did not submit the homework expect to receive based on this predicted line equation?

58.25

Which of the following is not an assumption for the multiple linear regression model (as we have learned it in this course)? -The errors have the same variance across all independent variable values. -The errors are normally distributed. -All of the errors are positive. -The errors have a true mean of 0. -The errors are independent of each other.

All of the errors are positive

Determine if y is linear to x

B1=0 B2≠0

Testing overall adequacy (stat. utility) of MLR model

B1=B2=0 At least one Bi≠0

Test whether the relationship between y and x1 depends on x1

B2=0 B2≠0 Use p value on top

In a test of whether or not to include interaction in our model, which parameter should we focus on? In other words, we are told to focus on a particular parameter to test for the presence of interaction. Which parameter is this? Note: By using the word "test" above, I mean a test of that beta (or B) with the null hypothesis being that the beta (or B) is equal to 0. This hypothesis is tested using a t-test (according to what we have learned).

B3: the slope for x1 times x2 (i.e., x1*x2)

Test whether relationship between y and x1 depends on x2

B3=0 B3≠0 Use p value on top

X < P-value

Fail to reject Ho

TRUE OR FALSE: In a multiple linear regression analysis, statistical model utility is determined by the value of R2 and 2s, while practical model utility is determined by the Global F-test p-value.

False

TRUE OR FALSE: There is never going to be and never has been a practical interpretation for the y-intercept of a predicted line equation in this course.

False

Suppose (hypothetically) that we have conducted a Simple Linear Regression for Exam 1 score by Homework 1 score and found the predicted line equation to be y_hat = 58.25 + 2.25x, where x represents Homework 1 score and y represents Exam 1 score. Provide a practical interpretation of the slope estimate above.

For each 1-point increase in Homework 1 score, we expect a 2.25 point increase in Exam 1 score.

What does it mean for two independent variables (say, x1 and x2) to interact in a multiple linear regression model?

It means that the slope in the relationship between x1 and y is a function of x2

Which of the following statistics provides us with a measure of the variation in the dependent variable explained by the Simple Linear Regression model?

R-squared

X > P-value

Reject Ho

Which of the following is NOT an assumption of Simple Linear Regression (SLR)? -The errors have a true mean of 0. -The dependent variable has the same variance across all values of the independent variable. -The errors follow a normal distribution. -The errors are independent of each other. -The dependent variable is qualitative.

The dependent variable is qualitative

TRUE OR FALSE: A prediction interval provides us with an interval estimate for the value of a single new observation for a given value of x.

True

LS line

Y-hat = B^0 + B^1(x)