Math 2208 Quiz 4 Plots & Regression Analysis Due Oct. 13 in Class Name: Question 1 Histogram of data 2 Histogram of data 1 16 12 14 10 12 Frequency Frequency 18 14 8 6 10 8 6 4 4 2 2 0 0 2 4 0 6 0 3 6 data 2 data 1 9 12 Histogram of data4 180 160 160 140 140 120 120 Frequency Frequency Histogram of data 3 180 100 80 40 40 20 20 3 4 5 6 7 8 9 80 60 2 100 60 0 0 -3 0 3 6 9 12 15 data4 data 3 a) (2 pts) Histograms for four data sets are above. Based on the histograms decide whether a normal model is appropriate, or not. Circle the correct answer. Data set 1: Normal model appropriate? Yes No Data set 2: Normal model appropriate? Yes No Data set 3: Normal model appropriate? Yes No Data set 4: Normal model appropriate? Yes No b) (1 pt.) Here are normal probability pots for the histograms on the left (data sets 1 & 3). Identify which NP plot belongs with which data set. Plot A belongs with data set? ________ Plot B belongs with data set? __________ Probability Plot B Probability Plot A Normal - 95% CI Normal - 95% CI 99 99.99 95 90 95 80 80 Percent Percent 99 50 20 60 50 40 30 20 5 10 1 70 5 1 1 0.01 ?? ?? Quiz 4 (Take home) Plots & Regression Analysis Name: Question 2: We are interested if there is an association between mileage (in thousands miles) and selling prices (thousands dollars) of used cars of the same model. Below is a table of data for eight cars. Mileage Price A 21 16 B 34 11 C 41 13 D 43 14 E 65 10 Here is the Minitab output for the regression. You may assume all relevant assumptions and conditions are satisfied. S = 1.87856 R-Sq = 70.4% G 76 7 H 84 7 Fitted Line Plot Price = 17.69 - 0.1181 Mileage S R-Sq R-Sq(adj) 16 Regression Analysis: Price versus Mileage 1.87856 70.4% 65.5% 14 Price The regression equation is Price = 17.69 - 0.1181 Mileage F 72 12 R-Sq(adj) = 65.5% 12 10 8 6 20 30 40 50 60 70 80 90 Mileage Use the Minitab results to help answer the following questions: 1) State the regression line. 2) What is y-intercept? Interpret it. Does it make sense? 3) Calculate the predicted price for observation F. 4) Calculate the value of the residual for observation F. 5) On the plot above, circle observation F and indicate the residual. 6) The best interpretation for the value of the slope is: A. B. C. D. E. F. Predicted mileage decreases by 0.1181 thousand miles for every 1000 dollars. Predicted price increases by 0.1181 thousand dollars for every 1000 miles. Predicted price decreases by 0.1181 thousand dollars for every 1000 miles. As mileage goes up, the price goes down. A strong negative linear association exists between mileage and price. Predicted price decreases by 17.69 thousand dollars when mileage increases by 1000 miles. 7) If the above regression were used to predict the price for mileage of 100,000 miles, the result would be: A. B. C. D. E. F. Unreliable, because the scatter plot has no outliers. Reliable, because the regression equation was used for the prediction. Reliable, since a large amount of distance variability is explained by year. Reliable, because the association is approximately linear. Unreliable, because this mileage was not in the study. Unreliable, because this mileage is outside the range of the observations. 2 Quiz 4 (Take home) Plots & Regression Analysis Name: 8) Interpret R2. 9) Calculate the correlation coefficient for this data. 10) Explain how to use the residual plot to check the conditions. Bonus Question: Male basset hounds have an average height of 34.5 cm with a standard deviation of 2 cm. Using the approximation rule for the normal model, give two values so that 95% of the dogs have heights between these values. Indicate the relevant proportions (percentages) by shading the appropriate area. 3