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simple linear regn

simple linear regn - Practice Problems for Simple Linear...

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© 2010 Radha Bose FSU Department of Statistics Practice Problems for Simple Linear Regression — 1 1. The average February temperatures for some European cities had mean 32.5 o F with standard deviation 12.3 o F. The latitudes of those cities had mean 41.2 o with standard deviation 5.8 o . The linear correlation between ave Feb temp and latitude was -0.864 (moderately strong). (i) Find the regression equation for predicting ave Feb temp from latitude. (ii) The correlation is moderately strong, so we may use the regression equation to make predictions. Use your regression equation to predict the ave Feb temp at 45 o latitude. (iii) If the correlation had been weak, say r=-0.269, what would have been our predicted ave Feb temp at 45 o latitude? (iv) Would it be appropriate to use your model to predict ave Feb temp in Berlin? State YES or NO and give a reason for your answer. (v) Would it be appropriate to use your model to predict ave Feb temp at a city whose latitude was 10 0 south of the equator? State YES or NO and give a reason for your answer. (vi) Fill in the blanks with numbers to make true statements: (a) For every degree increase in latitude, the decrease in predicted ave Feb temp is __________. (b) At zero degrees latitude, the predicted ave Feb temp is __________. (c) The proportion of variation in ave Feb temp that is explained by the linear association with latitude is __________. (vii) Does the y-intercept of the regression line have meaning in this context? State YES or NO and give a reason for your answer. (viii) If the residual for a certain city is negative , would you expect the city to be hotter or colder than predicted by the model, and why? (A) Colder, because the model is overestimating the ave Feb temp. (B) Colder, because the model is underestimating the ave Feb temp. (C) Hotter, because the model is overestimating the ave Feb temp. (D) Hotter, because the model is underestimating the ave Feb temp. 2. (Data adapted from Mann.) A team manager carried out a linear regression analysis to help him predict the percentage of games a team wins from its total payroll (in millions of dollars). The linear correlation between total payroll and percentage of wins was found to be -0.404 and the regression equation was x y 23 . 0 35 ˆ - = . Write out the correct interpretations of R 2 , the y-intercept and the slope in the context of the problem. Be sure to quote the numerical value of R 2 , the y-intercept and the slope in your interpretations.
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© 2010 Radha Bose FSU Department of Statistics Practice Problems for Simple Linear Regression — 2
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