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 3
Investigate whether mother’s pre-pregnancy weight and birth weight are associated using a scatterplot, correlation and simple regression

4. Exercise 3: correlation
Pearson’s correlation coefficient =
Describe the relationship using the scatterplot and correlation coefficient

5. Exercise 3: 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)?

6. Exercise 3: Regression Pre-pregnancy weight coefficient and p-value:
Regression equation:
Interpretation:

7. Exercise 4: correlations
Which variables are most strongly related to each other?

8. Exercise 5
Run a multiple regression model for Birth weight with gestational age, mothers weight and smoking status as independent variables
Check the assumptions and interpret the output
Does the model give more reliable predictions than the model with just gestational age?
Add mother’s height to the model. Does anything change?
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)

9. Exercise 5: model 1 summary
Variable
Coefficient (β)
P-value
Significant?
Constant
Gestation
Smoker
Pre-pregnancy weight
Adjusted R2 =
Interpretation:

10. Exercise 5: model 2 summary
Variable
Coefficient (β)
P-value
Significant?
Constant
Gestation
Smoker
Pre-pregnancy weight
Height
Adjusted R2 =
Interpretation:

11. Exercise 5: Compare p-values
Model
Gestation
Smoking
Weight
Height
P < 0.001
+ Smoker
0.028
+ Weight
+ Height

12. Exercise 5: Compare R2 Model R2 Adjusted R2 Gestation 0.499 0.486
+ Smoker
0.558
0.535
+ Weight
+ Height

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

14. 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.

15. Exercise 3: scatterplot
Assumption 1: Is there a linear relationship?
Yes!

16. Exercise 3: 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

17. Exercise 3: 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

18. Exercise 3: 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.

19. Exercise 3: normality of the residuals?
Yes – histogram roughly peaks in the middle

20. Exercise 3: homoscedasticity?
Yes – no patterns in residuals

21. Exercise 4: 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

22. Exercise 5: Model 1 residual assumptions
Assumptions are met

23. Exercise 5: Model 1 Adjusted R2
Does the model result in reliable predictions?
Yes – the adjusted R2 is reasonably high

24. Exercise 5: Model 1 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

25. Exercise 5: Model 1 regression coefficients
Gestational age (p < 0.001), mother’s pre-pregnancy weight and smoking status (p=0.016) are significant predictors of birth weight after controlling for the weight and height of the mother. Weight increases by 0.14 kgs for each week of gestation, by 0.02 kgs for each extra kg a mother weighs and decreases by 0.31 kgs for smokers.

26. Exercise 5: Model 2 (including height)
There’s a moderate positive linear relationship between maternal height and birth weight.

27. Exercise 5: Model 2 residual assumptions
Assumptions are met

28. Exercise 5: Model 2 Adjusted R2
Does the model result in reliable predictions?
Yes – the adjusted R2 is reasonably high

29. Exercise 5: 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

30. Exercise 5: Model 2 regression coefficients
Interpretation:
Gestational age (p < 0.001) and smoking status (p=0.016) are significant predictors of birth weight after controlling for the weight and height of the mother. Weight increases by 0.14 kgs for each week of gestation and decreases by 0.31 kgs for smokers.

31. Exercise 5: compare p-values
Model
Gestation
Smoking
Weight
Height
P < 0.001
+ Smoker
0.024
+ Weight
0.016
0.025
+ 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.

32. Exercise 5: compare Adjusted R2
Model R2
Adjusted R2
Gestation
0.502
0.489
+ Smoker
0.563
0.541
+ Weight
0.618
0.588
+ 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