Main focus of this material is to familiarize student with following learning objectives: Strength of Correlation, direction of correlation, curvilinear correlation, correlation coefficient, pearson's correlation coefficient, significance of scatter plots, partial correlation, Regression Model, Interpreting Regression Line, Prediction errors, Regression and Pearson's correlation, regression and analysis of variance, multiple regression. Select one or a combination of methods above to solve 3 problems below.
1) Nine patients with anaemia had their blood drawn to compute two blood components. Results were:
|
Patient
|
x (# of type A)
|
y (# of type B)
|
|
1
|
36
|
17
|
|
2
|
20
|
31
|
|
3
|
3
|
18
|
|
4
|
3
|
27
|
|
5
|
2
|
21
|
|
6
|
30
|
23
|
|
7
|
0
|
7
|
|
8
|
10
|
21
|
|
9
|
22
|
20
|
NOTE: ∑x = 126 ∑y=185 ∑x^2=3202 ∑y^2= 4163
1) Determine [Pearson] correlation between numbers of type A and number of type B. Then test to see whether it considerably varies from 0 [use alpha = 5%]. Don't forget to identify the null and alternative hypotheses.
2) Assume that you did a study which found that number of major crimes in cities is positively correlated [p<.001] to number of automobiles driven in city. One reader sent you following note: based on your work, if we want to make cities safer, one way would be to limit number of cars. What would you react?
p<.001 means that result is significant even with alpha = .001. For comparison, p=.05 would point out that result is significant with alpha =.05 BUT not for something smaller such as alpha = .01