Statistics: Regression analysis

Question 1

Give another name for a regression equation

Answer 1

A prediction equation

Question 2

What is meant by a model in statistics

Answer 2

a simple approximation of how variables relate in population

Question 3

What is meant by a conditional distribution?

Answer 3

The probability of y values at a fixed value of x

Question 4

When you have several quantitative variables what can software provide?

Answer 4

A correlational matrix

Question 5

Describe the relationship between x and y in regards to their distance from the mean

Answer 5

If an x value is a certain number of standard deviations from the mean the y value is r times that many standard deviations from its mean

Question 6

show two forms of predictions error

Answer 6

• The error using the regression line to make a prediction (y-y^)
• The error using the mean of y to make a prediction (y- mean of y)

Question 7

What formula do you use to summarize the size of the errors in each scenario?

Answer 7

total sum of squares for means, residual sum of squares for regression equation

Question 8

How do we eliminate the dependance of units when summarising errors?

Answer 8

by calculating the proportional reduction in error using r^2 formula

Question 9

what does it mean if r^2= 0.6?

Answer 9

The error using y^ to predict y is 60% smaller than the error using the mean of y to predict y.

Question 10

Name two disadvantages of r^2

Answer 10

• It’s easier to interpret the original scale than a squared scale
• The direction of the relationship is lost

Question 11

Name two factors that have strong influence on on the size of the correlation apart from outliers

Answer 11

• If the subjects are grouped for the observations rather than individually the correlation tends to increase in magnitude
• The size of the correlation depends on the range of the x values sampled. The correlation is smaller when we sample only a restricted range of x values than when we use the entire range.

Question 12

What is the name given to the error of making predictions about individuals based on the summary results of groups?

Answer 12

Ecological fallacy

Question 13

State the basic assumption for for using a regression line for description

Answer 13

The population means of y at different values of x have a straight line relationship with x in the form my=a+Bx

Question 14

State the extra assumptions for using regression to make statistical inference

Answer 14

• Data was gathered using randomisation

- The population values of y at each value of x follow a normal distribution, with the same sd at each x value

Question 15

What is the null hypothesis that x and y are statistically independent?

Answer 15

H0:B=0

Question 16

What does a small p value mean in this context

Answer 16

The regression line has a non zero slope

Question 17

How do you find the d value in this calculation and for the confidence interval?

Answer 17

n-2

Question 18

When may a confidence interval for B not have a useful interpretation? what do we do in this situation?

Answer 18

If a one unit increase in x is relatively small or large, we can then estimate the effect for an increase in x that is a more relevant portion of the actual range of x values