Suppose that you are trying to predict the GPA of Cuesta College student with the following variables: 1. The number of credits that a student takes per semester. (Number of Credits) 2. The number of hours that a student spends in the tutoring center. (Tutoring Hours) 3. The number of hours that a student works at a job. (Number of Job Hours) After you perform a linear regression analysis of all three relationships, you discover that all three trends are linear with the following correlation coefficients: Number of Credits and GPA: r= 0.75 Number of Tutoring Hours and GPA: r= 0.80 Number Job Hours and GPA: r=-0.90 Which of the variables is the best predictor of a student's GPA? Number of Tutoring Hours Number of Job Hours Number of Credits
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We want to be able to predict the G.P.A. of students by the number of hours that they spent on homework per week. The chart below shows the relationship for 6 students Hours per week spent on homework (x) GPA for the term (y) 15 2.0 28 3.7 13 2.7 20 3.0 4 0.9 10 2.0 What is the correlation coefficient? Is there a linear relationship between hours spent on home work and GPA at .05 significance level? Why? Assuming that there is a linear relationship, what is the line that describes the relationship? If a student spent 30 hours per week studying, what would you expect their GPA to be given the relationship in part d? What would you expect their GPA to be if there were no linear relationship?
Sheryl E.
'Suppose local university researcher wants to build linear model that predicts the freshman year GPA of incoming students based on high school SAT scores. The researcher randomly selects sample of 40 sophomore students at the university and gathers their freshman year GPA data and the high school SAT score reported on each of their college applications He produces a scatterplot with SAT scores On the horizontal axis and GPA on the vertical axis. The data has linear correlation coefficient of 0.454012. Additional sample statistics are summarized in the table below: Variable Sample Sample standard Variable description mean deviation high school SAT score x =1503.578103 Sx = 107.836402 freshman year GPA y = 3.299812 0.517403 r = 0.454012 slope 0.002178 Determine the y-intercept; a, of the least-squares regression line for this data. Give your answer precise to four decimal places. Avoid rounding until the last step.'
Sri K.
The line of best fit for the data can be modeled by the equation: Grade = 0.6 * Hours + 47 (r = 0.91) Using the given model, determine a student's grade in the course if they study for 70 hours during the semester. Round to the nearest tenth. Using the given model, determine the number of hours a student would need to study to earn a grade of 72% in the course. What can a student expect their grade to be if they study for zero hours all semester? How much can a student expect to improve their grade for each additional hour they study? Do you feel there is a causal relationship between the two variables?
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