1. Exercise 1: Gestational age and birthweight
Draw a line of best fit through the data (with roughly half the points above and half below). Describe the relationship
Is the relationship:
strong/ weak?
positive/ negative?
linear?

2. Exercise 2: Interpretation
Interpret the following correlation coefficients using Cohen’s classification and explain what they mean. Which correlations seem meaningful?
Relationship
Correlation
Average IQ and chocolate consumption
0.27
Road fatalities and Nobel winners
0.55
Gross Domestic Product and Nobel winners
0.70
Mean temperature and Nobel winners
-0.60

3. Exercise 3a: Scatterplot
Use Recode > Transform into Different Variables to construct a variable for maternal smoking status (non-smoker / smoker)
Construct a scatterplot for birthweight and gestational age? Use Set Markers by to distinguish between smokers and non-smokers
Is there evidence of a linear relationship
Interpret the correlation coefficient. What does it mean?
Note:
Think about which variable should be on the x axis (horizontal) and which should be on the y axis( vertical)
If you double-click on the graph you can open the Graph dialog window and edit the chart, for example change the colours used for smokers and non-smokers

4. Exercise 3b: Scatterplot & Correlation
Construct a scatterplot and calculate Pearson’s correlation coefficient for birthweight and maternal pre- pregnancy weight?
Is there evidence of a linear relationship
Interpret the correlation coefficient. What does it mean?
Note: think about which variable should be on the x axis (horizontal) and which should be on the y axis( vertical)

5. Exercise 4
Investigate whether mother’s pre-pregnancy weight and birth weight are associated using a simple linear regression

6. Exercise 4: regression Adjusted R2 =
Does the model result in reliable predictions?
ANOVA p-value =
Is the model an improvement on the null model (where every baby is predicted to be the mean weight)?

7. Exercise 4: Regression Pre-pregnancy weight coefficient and p-value:
Regression equation:
Interpretation:

8. Exercise 5
Re-run the regression model, but this time, produce the residual plots. Do you think that the assumptions of normality of residuals and homogeneity of variance are met?

9. Exercise 6: correlations
Produce a correlation matrix for the correlations between Birthweight, Gestational age, Maternal height and Maternal pre-pregnancy weight: Analyse > Correlate > Bivariate & add the 4 variables to the Variables box:

10. Exercise 7
With birthweight as the outcome, run a series of regression models:
Model 1: Gestational age
Model 2: Gestational age and maternal smoking status
Check the assumptions and interpret the output of
Does the model give more reliable predictions than the model with just gestational age?
Model 3: gestational age, maternal smoking status, maternal pre-pregnancy weight
Model 4: gestational age, maternal smoking status, maternal pre-pregnancy weight, maternal height
Note you will need to create a variable for smoking status based on the number of cigarettes that the mother smokes (assuming that 0 cigarettes indicates someone who does not smoke)

11. Exercise 7: model 1 summary
Variable
Coefficient (β)
P-value
Significant?
Constant
Gestation
Adjusted R2 =
Interpretation:

12. Exercise 7: model 2 summary
Variable
Coefficient (β)
P-value
Significant?
Constant
Gestation
Smoker
Adjusted R2 =
Interpretation:

13. Exercise 7: model 3 summary
Variable
Coefficient (β)
P-value
Significant?
Constant
Gestation
Smoker
Pre-pregnancy weight
Adjusted R2 =
Interpretation:

14. Exercise 7: model 4 summary
Variable
Coefficient (β)
P-value
Significant?
Constant
Gestation
Smoker
Pre-pregnancy weight
Height
Adjusted R2 =
Interpretation:

15. Exercise 7: Compare p-values
Model
Gestation
Smoking
Weight
Height
Model 1:
P < 0.001
Model 2:
Model 1 + Smoker
0.028
Model 3:
Model 2 + Weight
Model 4:
Model 3 + Height

16. Exercise 7: Compare R2 Model R2 Adjusted R2 Model 1: Gestation 0.499
0.486
Model 2:
Model 1 + Smoker
0.558
0.535
Model 3:
Model 2 + Weight
Model 4:
Model 3 + Height

17. Exercise 1: Gestational age and birthweight
There is a strong positive relationship which is linear

18. Exercise 2: Interpretation
Relationship
Correlation
Interpretation
Average IQ and chocolate consumption
0.27
Weak positive relationship. More chocolate per capita = higher average IQ
Road fatalities and Nobel winners
0.55
Strong positive. More accidents = more prizes!
Gross Domestic Product and Nobel winners
0.7
Strong positive. Wealthy countries = more prizes
Mean temperature and Nobel winners
-0.6
Strong negative. Colder countries = more prizes.

19. Exercise 3a: Scatterplot

20. Exercise 3b: scatterplot
Is there a linear relationship?
Yes!

21. Exercise 3b: correlation
Pearson’s correlation = 0.40 Describe the relationship using the scatterplot and correlation coefficient: There is a moderate positive relationship between mothers’ pre-pregnancy weight and birth weight (r = 0.40). Generally, birth weight increases as mothers weight increases

22. Exercise 4: regression
Adjusted R2 = 0.14 Does the model result in reliable predictions? Not really. The adjusted R2 value is ANOVA p-value = Is the model an improvement on the null model (where every baby is predicted to be the mean weight)? Yes as p < 0.05

23. Exercise 4: regression
Pre-pregnancy weight coefficient & p-value: (p = 0.009) Regression equation: y = Interpretation: There is a significant relationship between a mothers’ pre-pregnancy weight and the weight of her baby (p = 0.009). Pre-pregnancy weight has a positive affect on a baby’s weight with an increase of kg for each extra kg a mother weighs.

24. Exercise 5: normality of the residuals?
Yes – histogram roughly peaks in the middle

25. Exercise 5: homoscedasticity?
Yes – no patterns in residuals

26. Exercise 6: correlations
Which variables are most strongly related to each other?

27. Exercise 6: correlations
Which variables are most strongly related?
Gestation and birth weight (0.708)
Mothers height and weight (0.681)
Mothers height and weight are strongly related. They don’t exceed 0.8 but try the model with and without height in case it’s a problem

28. Exercise 7: model 1 summary
Variable
Coefficient (β)
P-value
Significant?
Constant
-3.029
0.004
Yes
Gestation
0.162
< 0.001
Adjusted R2:
Interpretation: As p < 0.05, gestational age is a significant predictor of birth weight. Weight increases by 0.16 kgs for each week of gestation

29. Exercise 7: model 2 summary
Variable
Coefficient (β)
P-value
Significant?
Constant
-2.661
0.009
Yes
Gestation
0.162
< 0.001
Smoker
-0.298
0.024
Adjusted R2: Interpretation: As p < 0.05 for both smoking status and gestational age both are significant predictors of birth weight. Weight increases by 0.16 kgs for each week of gestation. Mothers who smoke have, on average babies who weigh 0.30kgs less than babies born to mothers who do not smoke.

30. Exercise 7: Model 2 residual assumptions
Assumptions are met

31. Exercise 7: Model 2 ANOVA ANOVA p-value < 0.001
Is the model an improvement on the null model (where every baby is predicted to be the mean weight)? Yes as p < 0.05

32. Exercise 7: Model 2 Adjusted R2
Does the model result in reliable predictions?
Yes – the adjusted R2 is reasonably high

33. Exercise 7: model 3 summary
Variable
Coefficient (β)
P-value
Significant?
Constant
-3.268
0.001
Yes
Gestation
0.142
< 0.001
Smoker
-0.305
0.016
Pre-pregnancy weight
0.020
0.025
Adjusted R2: Interpretation: As p < 0.05 for all variables, all are significant predictors of birth weight. Weight increases by 0.14 kgs for each week of gestation. Mothers who smoke have, on average babies who weigh 0.30kgs less than babies born to mothers who do not smoke, and for each increase in pre- pregnancy weight of 1kg, babies weight increases by 0.02kgs, or 20gms. It is worth noting that whilst this is significant, it makes very little difference to birthweight in practice.

34. Exercise 7: model 4 summary
Variable
Coefficient (β)
P-value
Significant?
Constant
0.015
Yes
Gestation
0.141
< 0.001
Smoker
-0.306
0.016
Pre-pregnancy weight
0.013
0.263 No
Height
0.012
0.366
Adjusted R2:
Interpretation: P < 0.05 for gestational age and smoking status. However, now that maternal height has been added to the model, neither pre-pregnancy weight nor height are significant. They are strongly related and are sharing some of the variation in birth weight when both in the model.

35. Exercise 7: Compare p-values
Model
Gestation
Smoking
Weight
Height
Model 1:
< 0.001
Model 2:
Model 1 + Smoker
0.024
Model 3:
Model 2 + Weight
0.016
0.025
Model 4:
Model 3 + Height
0.263
0.366
Smoking gets more significant as variables are added.
Mothers’ weight becomes non-significant once height has been added. They are strongly related and are sharing some of the variation in birth weight when both in the model.

36. Exercise 7: Compare R2
Model R2
Adjusted R2
Model 1:
Gestation
0.502
0.486
Model 2:
Model 1 + Smoker
0.563
0.541
Model 3:
Model 2 + Weight
0.618
0.588
Model 4:
Model 3 + Height
0.627
0.586
Adding smoker and weight improves the fit a little bit
Adding height has not improved the fit of the model at all as the adjusted R2 decreases