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Practice Problems chapter 11

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Question;Practice Problems: Chapter 12;(part E is worth 3 points--all other parts;of the question are worth 1 point);1) A);Provide detailed;reasoning why or why not Regression is appropriate using just the scatterplot;and correlation given below.;Correlations;Taxes, size (Taxes in dollars, size in;square feet);Pearson;correlation of Taxes and size = 0.738;P-Value = 0.000;B) Given the Regression Equation below indicate the explanatory;variable and the response variable.;Regression;Analysis: Taxes versus size;The regression;equation is;Taxes = - 372 +;1.34 size;C) What is the;y-intercept? Does the y-intercept have;any logical interpretation? We cannot;logically interpret the y-intercept unless we have data points at X = 0 in the;data set. If in fact we cannot;logically interpret the y-intercept, then the y-intercept is only useful for;positioning the line properly in the plot.;So, the question hinges on whether we have data points at X=0 in the;data set.;Regression;Analysis: Taxes versus size;The regression;equation is;Taxes = - 372 +;1.34 size;D) What is the slope coefficient?;What is the slope interpretation?;Be specific (ie: for each unit increase in ____, we expect;to increase/decrease by _____).;Regression;Analysis: Taxes versus size;The regression;equation is;Taxes = - 372 +;1.34 size;E)What is the;predicted Tax value for a house of size 2,000 square feet? Show all work.;Regression;Analysis: Taxes versus size;The regression;equation is;Taxes = - 372 +;1.34 size;F) From the output below can we conclude that size is a significant;linear predictor of real estate taxes?;In answering this question, first provide the null and alternative;hypothesis being tested. Then;calculate the test statistic using the values in the output (show all;work). Finally, indicate the p-value of;our test statistic and the conclusion and reasoning behind your conclusion.;Predictor Coef;SE Coef T P;Constant -372.2;200.6 -1.86 0.067;size 1.3368;0.1235 10.82 0.000;S = 684.635 R-Sq = 54.5% R-Sq(adj) = 54.0%;G) The R2value is 54.5%. Provide a detailed description of what an R2;of 54.5% indicates.;H) What are the FIT (fitted values) and what are the RESI;(Residuals)? Be specific.;I) Describe why we use a Residuals vs Fitted Values scatterplot to;test for constant variance. (see figure;12.4 in the text) Remember, the fitted;values (the values on the line) are the mean Y values for the given X value and;we expect the observed Y values to be equally distributed around each and every;X value.;J) Given the Residuals vs Fitted values scatterplot below is the;constant variance assumption appropriate?;K) Why do we want the Residuals to be;normally distributed?;Given the Probability Plot below are these;Residuals normally distributed?;L);Given the X value of 2,500 square feet--you are given a 95% confidence;interval for?y and a prediction interval. What do each of these indicate?;Predicted Values;for New Observations;New;Obs Fit;SE Fit 95% CI 95% PI;1;2969.8 138.4 (2695.2, 3244.5) (1583.7, 4356.0);Values of;Predictors for New Observations;New;Obs size;1 2500

 

Paper#62274 | Written in 18-Jul-2015

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