A regression line is fit to 75 data points relating study hours (x) to exam scores (y). The resulting line is ŷ = 50 + 75x with r² = 0.85. A new data point (x = 2, y = 98) is added to the dataset. (a) Does this point appear to be an outlier? Explain using the regression line. (b) Would this point likely be influential? Explain what "influential" means in regression context. (c) After adding this point, would you expect r² to increase, decrease, or stay the same? Explain.
Answer:
A regression line is fit to 21 data points relating study hours (x) to exam scores (y). The resulting line is ŷ = 50 + 15x with r² = 0.85. A new data point (x = 2, y = 98) is added to the dataset. (a) Does this point appear to be an outlier? Explain using the regression line. (b) Would this point likely be influential? Explain what "influential" means in regression context. (c) After adding this point, would you expect r² to increase, decrease, or stay the same? Explain.
Answer:
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