W7 Regression Analysis

Question 1

What is Regression Analysis?

Answer 1

• Regression is concerned with predicting one variable from another related variable

Question 2

What are three ways regression is different to correlation?

Answer 2

1. The purpose
2. How we describe our variables
3. The inferential tests
   a. R2 (squared) value
   b. Regression coefficient (b value)
   c. Intercept (a value)

Question 3

What is the point of the regression line (line of best fit)?

Answer 3

• The regression line minimises the vertical deviations of the points from the line.
• Basically by minimising the vertical distance the points are from the line minimises the error of prediction

Question 4

What is the Bivariate Regression Equation?

Answer 4

• The bivariate regression equation uses two variables to predict each other
• Y= a + bX
  Y = dependent variable
  a = constant (Y intercept) - occasionally represented as ‘c’
  b = regression coefficient (slope)
  X = independent variable

Question 5

How do you find the ‘a’ value (Y intercept) and the ‘b’ value (the slope of the line)?

Answer 5

• To find ‘a’ value look along Y axis (vertical) and see where the line intercepts it
• To calculate ‘b’ value you do: Change in Y divided by Change in X or (Y-Y1) / (X-X1)

Question 6

How is variability checked within regression analysis?

Answer 6

• You use R2 (squared)
• To check the variance between the dependent variable and independent variable use R2 (squared)
• Square the correlation coefficient
  E.g. R = 0.62
  R2 (squared) = 0.38, so the dependent variables explains 38% of the variance in the independent variable

Question 7

What are the 7 steps to perform a regression analysis?

Answer 7

1. Null hypothesis (key thing with 1 & 2 is they are talking about predicting)
2. Alternative hypothesis
3. Select a level of significance (sig. is set at p<0.05)
4. Collect & Summarise data
5. Make sure to check all 6 assumptions
6. Run statistical test
7. Interpret significance of result

Question 8

Assumptions Check for Bivariate regression (point 5/7 steps to performing regression analysis):

• This is how we check our data to make sure it fits the crate for…
• What are the 6 assumptions to check for?

Answer 8

• …parametric & is normally distributed
  1. Normal distribution
  2. Homogeneity of variance
  3. Interval/ratio
  4. Independence
  5. Linear relationship
  6. Residuals are normally distributed (SPSS does this to make sure the bars in a bar chart fit roughly within a bell shaped curve)

Question 9

What does the R value on SPSS represent?

Answer 9

R value = simple correlation value (strong/positive)

R value = Pearsons correlation coefficient

Question 10

What does the R2 (squared) value on SPSS represent?

Answer 10

• R2 (squared) value = coefficient of determination OR the amount of variance explained.
• So if R2 (squared) was 0.81 that means the the variance that the independent variable was from the dependent variable can be explained as 81% (lots)

Question 11

What does the Sig. value on SPSS represent?

Answer 11

• The Sig. value represents if the data is statistically significance or not.
• Sig. is also shown as P value
• For data to be significant it must be below 0.05 (P<0.05)

Question 12

Describe where you can find the ‘a’ & ‘b’ values on an SPSS data sheet.

Answer 12

• ‘a’ & ‘b’ are both in the box labelled ‘B’
• The one by the ‘(Constant) = ‘a’ (Y intercept)
• The one by the ‘Sum.5skinfold’ = ‘b’ (Slope of regression line or steepness of the line of best fit)

Question 13

What does the ‘t’ statistic show you?

Answer 13

• The ‘t’ statistic shows you if the line of best fit is statistically significant from zero. So to see if there is a positive or negative correlation.
• You have to compare the ‘t’ statistic to the Sig. value