Final session 11b

Question 1

when to use Simple Linear Regression

Answer 1

When we want to summarize the linear relationship between two variables, X and Y

Question 2

how do we do Simple Linear Regression

Answer 2

We can do this by drawing a straight line on the scatterplot

Question 3

a straight line on the scatterplot is called what

Answer 3

regression line

Question 4

The regression line is a straight line that describes how what

Answer 4

Y changes as X changes

Question 5

For a given observation (i), our simple linear regression equation:

Answer 5

Yi = b0 + b1X1i + ei

Question 6

explain the parts to Yi = b0 + b1X1i + ei

Answer 6

Yi is the value of the DV for observation i X1i is the value of the IV for observation i ei is the residual for person i

Question 7

Residuals are called what in the population

Answer 7

errors

Question 8

whats assumed about Errors

Answer 8

assumed normally distributed with a constant variance

Question 9

How to determine the best regression line?

Answer 9

The “best” regression line is one that has the smallest residuals

Question 10

what is Residual

Answer 10

• “vertical” difference between the regression line and each data
  point

Question 11

what method is typically used determine the best regression line

Answer 11

Method of least squares

Question 12

what is Method of least squares

Answer 12

the most common method. The least-squares regression line of Y on X1 is the line that makes the sum of squared residuals as small as possible

Question 13

The least-squares regression line of Y on X1 is determined in such a way that it makes SSR ….

Answer 13

as small as possible

Question 14

b0 and b1 are determined todo what

Answer 14

minimize SSR

Question 15

what is the goal of least squares

Answer 15

In other words, this method aims to minimize the unexplained portion of Y by the regression line

Question 16

how to Simple regression used for prediction

Answer 16

Using our regression line, if we only had a value on X1, we could predict the value of Y

Plug in value of predictor(s) into the equation for the regression line

Question 17

what is the Statistical test for significance for

Answer 17

Often times it is of interest to test the relationship between Y and a predictor variable
If we call β1 the population value for b1, is β1 equal to zero in the population?

Question 18

Statistical test for significance of the slope: give the hypotheses

Answer 18

Typically we are testing this hypothesis:
H0 :β1 =0

There is no linear relationship between X1 and Y (no effect of X1 on
Y)
H1 :β1 ̸=0

There is a linear relationship between X1 and Y

Question 19

To test H0 for a slope, we also use what

Answer 19

a t-test of the form:

t = b1 − 0 / sb1

Question 20

what is the df for Statistical test for significance of the slope

Answer 20

dfR = N − 2

Question 21

the observed value of t is greater than a critical value of t with dfR = N − 2 (and α = .05), we may reject the null hypothesis
This indicates what

Answer 21

that the slope is significantly different from zero, suggesting a statistically significant effect of X1 on Y

Question 22

For the t-test to provide accurate results, the following assumptions are required:

Answer 22

Relationship between predictor and outcome is linear Independent observations
Homoscedasticity
Normally distributed errors

Question 23

what is Homoscedasticity

Answer 23

Variance of errors does not depend on the value of the predictor, X1

Question 24

(simple linear regression) As in ANOVA, we can also divide the variance (or variation) in the DV (Y ) into different parts resulting from different sources
In regression analysis, the total variation in Y is partitioned into:

Answer 24

SSM : The variation in Y that is explained by the model (i.e., regression line)
SSR: The variation in Y that is unexplained by the regression line (i.e., the residuals)
SST : Total amount of variation in Y

SST =SSM +SSR

Question 25

for Simple Linear Regression, The F statistic can be used for testing what

Answer 25

whether the model overall significantly predicts the dependent variable

Question 26

The F statistic can be used for testing whether the model overall significantly predicts the dependent variable
In the case of a single predictor, what is the hypotheses

Answer 26

H0 :β1 =0 H1 :β1 ̸=0

Question 27

If the observed F ratio is greater than a critical value of F with dfM and dfR at α, we may _____ H0

Answer 27

reject

Question 28

explain Coefficient of Determination (R2)

Answer 28

Proportion of the total variation in Y accounted for by the model R2 = SSM / SST

Question 29

Coefficient of Determination (R2) Ranges from 0 to 1 explain

Answer 29

The larger R2, the more variance of the DV is explained 0 = No explanation
1 = Perfect explanation

Question 30

In simple regression, the relationship with Pearson correlation (r) is:

Answer 30

r2 = R2

Question 31

R2 is____ high; An adjusted value, R2 adj , is______

Answer 31

biased, unbiased