Stats lab
karlakay456
Math2150LProject2Fall2020.docxMath 2150L – Statistics Technology Lab – Project #2A – In Class Assignment
Tuesday March 3, 2020 Score ____________ / 50
PROBLEM 1 — IQ Scores (50 points – 10 points each part)
In studying the effects of heredity and environment on intelligence, it has been helpful to analyze the IQs of identical twins who were separated soon after birth. By studying identical twins raised apart, we can eliminate the variable of heredity and better isolate the effects of the environment. The table below shows the IQs of pairs of identical twins (older twins are x) raised apart.
|
Older Twin IQ |
107 |
96 |
103 |
93 |
96 |
113 |
86 |
99 |
109 |
105 |
96 |
|
Younger Twin IQ |
111 |
97 |
116 |
107 |
99 |
111 |
85 |
108 |
102 |
105 |
100 |
1) Provide the R coding for data entry and to create a publication worthy scatterplot. Once created insert the graph below.
2) Using R estimate and quantify Pearson’s correlation coefficient . (No R code needed, only report and quantify the value).
3) Provide the R coding that estimates the equation of the regression line using the older twin’s IQ as the predictor of the younger twin’s IQ. Be sure to only report the equation and its estimates, other output produced is not needed.
4) Use the regression equation reported in #3 to estimate the younger twin’s IQ given that the older twin had an IQ on the lower end, x= 90. Report the estimated younger twin’s IQ by entering the value in the table below. Repeat this estimation process given that the older twin had an IQ on the upper end, x = 120 and entering the estimated younger twin’s IQ in the table below. Of the two predictions, which is more reliable? Type your answer in the last row of the table.
|
Older Twin with IQ = 90 |
Estimated Younger Twin IQ =
|
|
|
|
|
Older Twin with IQ = 90 |
Estimated Younger Twin IQ =
|
|
|
|
|
More Reliable Estimate? (Type answer here) |
5) Find the coefficient of determination r2 and provide an interpretation.
PROBLEM 2 — Odds Ratio (50 points – 10 points each part)
A study investigated the effects of oral contraceptive (OC) use on heart disease in women 40 to 44 years of age. The results are displayed in the following table
|
|
Myocardial Infarction |
|
|
|
Yes |
No |
|
OC Users
|
13 |
4987 |
|
Non-OC Users
|
7 |
9993 |
1) In this study, who were more likely to experience myocardial infarction, OC Users or Non-OC Users? Answer Yes or No and briefly explain.
2) Provide the R coding that estimates the Odds of myocardial infarction for OC Users compared to Non-OC Users. Be sure to include the estimated OR value.
3) Provide the R coding that estimates the lower bound of a 95% confidence interval for the Odds Ratio in #4 above. Be sure to report the value.
4) Provide the R coding that estimates the upper bound of a 95% confidence interval for the Odds Ratio in #4 above. Be sure to report the value.
5) Explain what the data are showing with respect to OC use and myocardial infarction in this study.
