Question

12. We are interested in predicting a college freshman's GPA for their first semester from their overall ACT test score using a linear relationship. a) (4 pts.) Do we need to consider anything before we find the least squares line? If so, what and why? If not, why not? A b) (4 pts. Once we have calculated the least squares line we want to utilize it to predict a student's first semester GPA. Are there any concerns with utilizing this line for prediction or can we utilize this line for any values of ACT test scores? Explain your reasoning completely c) (5 pts. Now suppose we wish to estimate the slope of the least squares line utilizing a 95% confidence interval. Are any assumptions necessary? If so, what? If not, why not?

Answer 1

SOLO: Given Data before find the least need to considea la) Conditions LE Square line Cu can be (i) linearity : checked by con value near 1-0 The data should show a linews trend scatter plot and be evelating elation Coctficient which should strong ie absolute vd (ii) Alormally. The residuals should be be nearly normal Gin) Homa sladosti cenyo site wwability roughing (av) Independence - obscavation least square lire retrains cp the points around the constant independent of each other aye (b) need Conditions we to consider before predect a Studentis first year GPA W any G predict predict Student's first year GpA for Pn kertredake values of ACT test scorca (intu pokation) -jhe prediction is valid il Student's first year and for - he test Score ( extra polations rike prediction as nol valid ACT Outside given any

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