Homework Assignment 5 Q1

Homework Assignment 5 Q1. You are a researcher and would like to understand how substance use influences academic achievement. You are measuring substance use as the number of alcoholic drinks one has in a week and academic achievement as the number of hours one spends studying/doing homework a week. You take a sample of 300 CSUN students and ask them about their substance use and school/work habits. You decide to conduct a Bivariate Ordinary Least Squares (OLS) Regression to answer this question. (2.5 pts) • What is the independent variable? (The cause) • What is the dependent variable? (The effect) • Write a null hypothesis for this problem. • Write an alternative hypothesis for this problem. Q2. You decide to graph the data from Q1 and this is what you find. Number of Hours Spent Studying A Week Week Substance Use and Academic Achievement 8 7 6 5 4 3 2 1 0 0 1 2 3 Number of Drinks a Week 4 5 6 7 8 9 10 Answer the following questions (2.5 points). • What type of linear relationship is this? The value of the r correlation is -.34. • • • • What is the correlation interpretation/conclusion? What is the strength of the relationship (weak, moderate, strong)? What is the variance (r2)? What is the variance conclusion? Q3. You are interested in how family size effects impulsivity. You take a sample of 150 young adolescents, ages 12 – 18. You ask them how many people reside in their home, as well as administer a written assessment to test impulsivity. On this particular assessment, higher sores indicate more impulsivity and lower scores indicate lower impulsivity. Independent Variable: Number of people residing in the home. Dependent Variable: Impulsivity score. Null Hypothesis: Family size has no effect on impulsivity. Alternative Hypothesis: Youth with more people residing in the home are more impulsive. You decide to do a Bivariate Ordinary Least Squares Hypothesis Test. The alpha level is set at .05. Decision Rule: If the calculated p value is less than .05, you will reject the null hypothesis; if this is not the case, you will fail to reject the null hypothesis. The calculated p value is .023. The slope is calculated to be 2.223 Part I: (5 pts) • • • • • What is the hypothesis decision rule (reject the null hypothesis or fail to reject the null hypothesis)? Is this finding statistically significant? Interpret the results in a formal conclusion/what does this mean? Interpret the slope. What is the chance of error (type and percentage)? Same problem as above. You decide to do a Bivariate Ordinary Least Squares Hypothesis Test. The alpha level is set at .05. Decision Rule: If the calculated p value is less .05, you will reject the null hypothesis; if this is not the case, you will fail to reject the null hypothesis. The calculated p value is .067. Part II: (5 pts) • • • • What is the hypothesis decision rule (reject the null hypothesis or fail to reject the null hypothesis)? Is this finding statistically significant? Interpret the results in a formal conclusion/what does this mean? What is the chance of error (type and percentage)? *For assistance with Q1, Q2, and Q3, See Slides 64-67 of the Chapter 11 PowerPoint. Q4. According to the textbook (Chapter 12), what is multicollinearity? What causes multicollinearity? Why is multicollinearity a problem in Multiple Ordinary Least Squares (OLS) Regression?