1. Merve denizci nazlıgül, M.s.
Prediction
Merve denizci nazlıgül, M.s.

2. Scatter Plots
Regression uses exactly the same data as that used by correlation
Correlation considers how closely the data points fall to the line of best fit
In contrast, regression describes the characteristics of the straight line
We can develop a regression equation to predict the y value based on the x value

3. Making predictions
The independent variable is displayed on the horizontal axis (math ability)
The dependent variable is displayed on the vertical axis (music ability)
One can predict a person’s music ability based on their maths ability

4. Regression formula

5. Example 1
Case
Music score
Maths score 1 2 8 6 3 4 9 7 5 10

6. Regression output

7. Regression output

8. Interpretation
B is the slope (unstandardised regression coefficient in SPSS) = −.633
What this means is that for every increase of 1.00 on the horizontal axis, the score on the vertical axis changes by −.633.
The intercept (a; constant in spss) = 8.425,
It is the point at which the regression line cuts the vertical (y) axis.

9. Regression Equation
What would we predict the music ability to be for a person whose maths ability is 8?
Y = (−.53×8) = 8.43 – 5.04 = 3.39

10. Reporting output
A simple linear regression was calculated to predict MUSIC ABILITY (dependent variable) based on MATH ABILITY (predictor variable). A significant regression equation was found (F(1,8) = , p <.05) with an R2 of The math ability explained 81% of the variance in music ability.
Y = (−0.63X)
Where Y = the predicted music ability
8.43 is the intercept/constant
−0.63 is the gradient of the slope
X is a person’s maths ability

11. Example 2 Data set: regress
2.1.Does visiting to health professionals predict physical health symptoms? How much variance in physical health symptoms can be explained by scores on visiting to health professionals? Write the prediction equation.
2.2.Does physical health symptoms predict mental health symptoms? How much variance in mental health symptoms can be explained by scores on physical health symptoms? Write the prediction equation.
2.3.Does stressful life events predict mental health symptoms? How much variance in mental health symptoms can be explained by scores on stressful life events ? Write the prediction equation.
2.4.Does stressful life events predict physical health symptoms? How much variance in physical health symptoms can be explained by scores on stressful life events ? Write the prediction equation.

12. Reporting output
2.1. A simple linear regression was calculated to predict physical health symptoms based on visiting to health professionals. A significant regression equation was found (F(1,463) = , p <.05) with an R2 of The visiting to health professionals explained 19% of the variance in physical health symptoms .
X = Y
2.2. A simple linear regression was calculated to predict mental health symptoms based on physical health symptoms. A significant regression equation was found (F(1,463) = , p <.05) with an R2 of 255. The physical health symptoms explained 26% of the variance in mental health symptoms .
X = Y

13. Reporting output
2.3. A simple linear regression was calculated to predict mental health symptoms based on stressful life events. A significant regression equation was found (F(..,…) = ……, p <.05) with an R2 of …. The stressful life events explained …..% of the variance in mental health symptoms .
a + bX = Y
2.4. A simple linear regression was calculated to predict physical health symptoms based on stressful life events. A significant regression equation was found (F(..,…) = ……, p <.05) with an R2 of …. The stressful life events explained …..% of the variance in physical health symptoms .