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2.3-2.4 solutions

2.3-2.4 solutions - Stat 133 Recitation Solutions 2.3 and...

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Stat 133 Recitation Solutions 2.3 and 2.4 Regression (Part 1) (SOLUTIONS) We are comparing years of education and hours on the internet in the last month, to see if a relationship exists. If a relationship does exist, we want to predict Internet use using education level. The output is given below. Descriptive Statistics: Education, Internet Variable Mean StDev Variance Minimum Maximum Educatio 11.000 1.920 3.687 7.000 17.000 Internet 26.316 9.411 88.570 2.000 54.000 Pearson’s Correlation: 0.642 1. Interpret the correlation between Education and Internet use As Education increases so does internet use; the relationship is linear (need to check the scatterplot) but its strength is only moderate. 2. Would a line fit this data well? Explain by interpreting the correlation. A line would fit moderately well. 3. Define which variable is X and which one is Y. X is education since it is being used to predict Internet use (Y) 4. Find the slope of the best fitting line. b = r s y s x = .642 9.411 1.920 The slope is 3.15 This means as education increases by 1 year, internet usage increases by 3.15 hrs per month on average. 5. Find the Y-intercept of the best fitting line. a = y - bx = 26.316 - 11 3.15 ( 29 The Y-intercept is -8.29 This is not interpretable . 6. Find the equation of the best fitting line. Internet Use = -8.29 + 3.15 (Education) 7. Use the line to predict Internet use for someone with 16 years of education. Internet Use = -8.29 + 3.15 (16) = 42.11 hours per month (on average) *8. For what education levels is it appropriate to use this line to make predictions? Use the statistics given in the problem to answer this. Using the following row of the descriptive statistics for education given in the problem, you see that Education for the data collected is from 7 to 17 years. This is the range where you would feel most comfortable using Education (X) to predict Internet use (Y). Variable Mean StDev Variance Minimum Maximum Educatio 11.000 1.920 3.687 7.000 17.000 1

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Stat 133 Recitation Solutions 2.3 and 2.4 9. The linear regression of the computer output for the Internet/Education data is shown below. Use this output to find the equation of the best fitting line and use it to verify your answer to #6 above. Predictor Coef SE Coef T P Constant -8.290 2.665 -3.11 0.002 Education 3.1460 0.2387 13.18 0.000 Pick off the line from this output to be -8.29 + 3.15(X) = Y and verify your answer to #6 . Data was collected on amount of rainfall (inches) and amount of corn produced (bushels per acre) for a number of years in Kansas. The output is shown below. Predictor Coef SE Coef T P Constant 89.543 6.703 13.36 0.000 Rainfall 0.12800 0.01375 9.31 0.000 Correlation of Rainfall and Corn = 0.608 10. If rainfall increases by 1 inch, how much do you predict corn production will change by? a. 89.543 bushels per acre
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2.3-2.4 solutions - Stat 133 Recitation Solutions 2.3 and...

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