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Week 4 Assignment final project independent project
Intro to Biomedical Statistics (BST 322)
National University (US)
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Week 4 Assignment
- ( 1pt ) For each correlation coefficient below, calculate what proportion of variance is shared by the two correlated variables:
a. r = 0 = 0. b. r = 0 = 0.
c. r = 0 = 0. d. r = 0 = 0.
- ( 1pt ) For each coefficient of determination below, calculate the value of the correlation coefficient:
a. r 2 = 0 = 0. b. r 2 = 0 = 0.
c. r 2 = 0 = 0. d. r 2 = 0 = 0.
- ( 1pt ) Suppose a researcher regressed surgical patients’ length of stay (dependent variable) in the hospital on a scale of functional ability measured 24 hours after surgery. Given the following, solve for the value of the intercept constant and write out the full regression equation:
Mean length of stay = 6 days; mean score on scale = 33; slope = -0.
Y= 9 – 0
- ( 1pt ) Using the regression equation calculated in Exercise 3, compute the predicted value of Y (length of hospital stay) for patients with the following functional ability scores:
a. X = 42 Y= 9 – 0(42) = 5.
b. X = 68 Y= 9 – 0(68) = 3
- ( 4 pts ) Reexamine the Fellows Research Group data we used in week 2’s assignment (the excel file is named “ Fellows Mental Health Data ” and is also in this week’s assignment area). Using this data set again, perform a correlation analysis using the General Practitioner Assessment of Cognition score (“ GPCOG ”) as a predictor of the Mental Health Survey Score (“ MentalHlth ”) of all subjects.
a. Plot the data with a regression line and perform a regression with the appropriate statistical test in StatCrunch. Copy and paste your graph and regression output into your Word document for full credit.
b. What is the correlation coefficient r and what is the coefficient of determination here? What does the coefficient of determination mean in this case?
R (correlation coefficient) = 0. R-sq = 0. Meaning there is about 1% variance between the mental health and the GPCOG score
c. Is there a statistically significant correlation between cognition and mental health in this sample? No, there is not because the P-value is greater than 0.
d. What hypotheses did you test?
H0: Intercept = 0 HA: Intercept ≠ 0 H0: Slope = 0 HA: Slope ≠ 0
Simple linear regression results:
Dependent Variable: GPCOG Independent Variable: MentalHlth GPCOG = 8 + 0 MentalHlth Sample size: 150 R (correlation coefficient) = 0. R-sq = 0. Estimate of error standard deviation: 3.
Parameter estimates:
Paramet er
Estimate Std. Err. Alternativ e
DF T-Stat
Intercept 8 1 ≠ 0 14 8
Slope 0. 52
- 49
≠ 0 14 8
Analysis of variance table for regression model:
Sourc e
DF SS MS F-stat P- value Model 125. 6
6
5
Error 142263.
Yes, there is because the P-value is less than 0.
d. What hypotheses did you test?
H0: Intercept = 0 HA: Intercept ≠ 0 H0: Slope = 0 HA: Slope ≠ 0
e. Using StatCrunch, what is the predicted cholesterol level for a person taking a dose of 7 mg? Copy and paste your regression output from StatCrunch into your Word document for full credit. Predicted values:
- ( 5 pts ) A study by the University of Montreal examined a new test to deepen the evaluation of mental states through the creation and validation of a practical measure, the Mental States Task (MST). The researchers examined many factors including age and the valid and reliable PANAS test. The data is in an excel file named “ Montreal_Study_on_Mental_States ” and is also in this week’s assignment area. Using this data set, perform a correlation analysis using the subject’s age (“ AGE ”) as a predictor of their PANAS score (“ PANAS ”) of all the subjects.
a. Plot the data with a regression line and perform a regression with the appropriate statistical test in StatCrunch. Copy and paste your graph and regression output into your Word document for full credit.
b. What is the correlation coefficient r and what is the coefficient of determination here? What does the coefficient of determination mean in this case?
R (correlation coefficient) = 0. R-sq = 0. It means there is a 4% of variance between Age and PANAS.
c. Is there a statistically significant correlation between age and the PANAS score in this sample? Yes, because the p-value is less than 0.
Simple linear regression results:
Dependent Variable: PANAS Independent Variable: age PANAS = 0 + 0 age Sample size: 125 R (correlation coefficient) = 0. R-sq = 0. Estimate of error standard deviation: 0.
Parameter estimates:
Parameter Estimate Std. Err. AlternativeDF T-Stat P-value Intercept 0 0 ≠ 01231 0. Slope 0 ≠ 01232 0.
Analysis of variance table for regression model:
SourceDF SS MS F-stat P-value Model 15 5 0. Error 123107. Total 124 113. X value Pred. Y s.(Pred. y) 95% C. for mean 95% P. for new
X value Pred. Y s.(Pred. y) 95% C. for mean 95% P. for new 7 94 27(19, 170)(-87, 277)
d. What hypotheses did you test? H0: Intercept = 0 HA: Intercept ≠ 0 H0: Slope = 0 HA: Slope ≠ 0
f. Using StatCrunch, what is the predicted PANAS score for a subject that is 23 years old? Copy and paste your regression output from StatCrunch into your Word document for full credit.
Predicted values:
X value Pred. Y s.(Pred. y) 95% C. for mean 95% P. for new 23 2(2, 2)(0, 4)
- ( 1pt ) Use the multiple regression equation below for predicting graduate GPA for the two subjects below:
Y′ = -1 + 0(undergrad GPA) + 0(GREverbal) – 0(GREquant) +0(Motivation)
Subject undergrad GPA GREverbal GREquant Motivation 1 2 560 540 55 2 3 550 590 65
Subject 1: Y’ = -1 + 0 * 2 + 0 * 560 – 0 * 540 + 0 * 55 = 2. Subject 2: Y’ = -1 + 0 * 3 + 0 * 550 – 0 * 590 + 0 * 65 = 3.
- ( 1pt ) Using the following information for R 2 , k , and N , calculate the value of the F statistic for testing the overall multiple regression equation and determine whether F is statistically significant at the 0. level:
a. R 2 = 0, k = 5, N = 120 F=(0/5) / ((1-0)/(120-5-1)) = 3. Df1= 5 and Df2= Critical F(5,114) at 0.
b. R 2 = 0, k = 3, N = 64 F =(0/3) / ((1-0)/(64-3-1))=4.
Df1=3 and Df2= Critical F(3,60) at 0 level of significance = 2.
calculated F value 4 > critical F value 2. F is statistically significant.
Week 4 Assignment final project independent project
Course: Intro to Biomedical Statistics (BST 322)
University: National University (US)
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