10. Tell what each of the residual (a) (b) (c) plots to the ri...

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10. Tell what each of the residual (a) (b) (c) plots to the right indicates about the appropriateness of the linear - model that was fit to the data. - values N-values ! (a) Choose the best answer for residuals plot (a). A. The curved pattern in the residuals plot indicates that the linear model is not appropriate. The relationship is not linear. n. The residual plot indicates that most of the data fall roughly along a straight line, with the exception of a single point. c. The scattered residuals plot indicates an appropriate linear model. (b) Choose the best answer for residuals plot (b). A. The scattered residuals plot indicates an appropriate linear model. a The fanned pattern indicates that the lincar model is not appropriate. The model's predicting power decreases as the values of the explanatory variable increases. C. The residual plot indicates that most of the data fall roughly along a straight line, with the exception of a single point. (c) Choose the best answer for residuals plot (c). The fanned pattern indicates that the linear model is not appropriate. The model's predicting power increases as the values of the explanatory variable increases. D. The fanned pattern indicates that the linear model is not appropriate. The model's predicting power decreases as the values of the explanatory variable increases. C. The scattered residuals plot indicates an appropriate linear model. 9. .A. Annual GDP growth rates of developing countries (cont.) B. Annual GDP growth rates of developed countries C. Annual GDP growth rates of all countries D. Years 1968-2009 Scatterplot and Output of Regression Analysis 69 Ay 7. 6- 5- 4- 3- 2- 1- * o 1 2 3 4 5 6 Annual GDP Growth of Developed Countries (%) Dependent variable: GDP Growth Developing Countries R² - 18. .74% $ = 1.334 Variable Coefficient Intercept 3.56 GDP Growth Developed 0.458 Countries 9. The accompanying scatterplot shows the growth (in % of Gross Domestic Product) of the developing countries vs. the growth of developed countries for a particular region. Each point represents one of the years from 1968 to 2009. The output of a regression analysis follows the scatterplot. Complete parts a through c below. Click the icon to view the scatterplot and the output of the regression analysis. a) Check the assumptions and conditions for the linear model. What assumptions and conditions are met? A. All of the assumptions and conditions are met with the exception of the Quantitative Variables Condition: the data are categorical. B. All of the assumptions and conditions are met with the exception of the Lincarity Condition; the points do not follow a straight line pattern (as evidenced by the "-value). C. All of the assumptions and conditions are met with the exception of the condition that there are no outliers (there are a total of three outliers in the scatterplot). D. All of the assumptions and conditions are met. The variables are quantitative (with units % of GDP). the plot is reasonably straight, there are no outliers, and the spread is roughly constant (although the spread is large). b) Explain the meaning of R² in this context. A. About 19% of the variation in the growth rates of developing countries is caused by the growth rates of developed countries. B. About 19% of the variation in the growth rates of developed countries is caused by the growth rates of developing countries. C. About 19% of the growth rates of developing countries are accounted for by the growth rates of developed countries. D. About 19% of the variation in the growth rates of developing countries is accounted for by the growth rates of developed countries. c) What are the cases in this model? 8. f) If the sales for a price of $3.50 turned out to be 60,000 pounds, what would the residual bc? (cont.) The residual would be pounds. 8. A lincar model fit to predict weekly Sales of frozen pizza (in pounds) from the average Price (S/unit) charged by a sample of stores in a city in 39 weeks over a three-year period is shown below. Complete parts a through f. Sales = 140,506 - 24,878 Price a) What is the explanatory variable? Sales Price b) What is the response variable? Sales Price c) What does the slope mean in this context? A. Sales increase by 24,878 pounds per dollar. a Sales decrease by 24,878 pounds per dollar. C. Price increases by 24,878 dollars per pound. D. Price decreases by 24,878 dollars per pound. d) What does the y-intercept mean in this context? Is it meaningful? A. 140,506 pounds is a base value that is not meaningful because the price will not be SO. B. S 140,506 is a base value that is not meaningful because the sales will not be 0 pounds. C. 140,506 pounds is a base value that is meaningful because the price will be S0. D. $140,506 is a base value that is meaningful because the sales will be 0 pounds. c) What do you predict the sales to be if the average price charged was $3.50 for a pizza? The predicted sales would be pounds. 7. Here are several scatterplots. The calculated correlations are - 0.487, - 0.977, 0.006. and 0.777. (a) (b) Which is which? Match each scatterplot with its calculated correlation. (a) (c) (d) (b) (c) (d) 6. A Nonc of these scatterplots (cont.) D. Scatterplots 2 and 3 C. 2 D. Scatterplots 1 and 3 E. 1 F. All of these scatterplots d) Which scatterplot shows a weak or moderately strong association? A. Scatterplots 1 and 2 n. Scatterplots 2 and 3 C. 3 D. Scatterplots 1 and 3 E All of these scatterplots F. None of these scatterplots c) Which scatterplot shows a very, not just a moderately, strong association? A. Scatterplots 1 and 3 a. 1 C. 3 D. Scatterplots 2 and 3 E. Scatterplots 1 and 2 F. 2 6. Which of the seatterplots to the right show a) no association? b) a negative association? (1) c) a lincar association? d) a weak or moderately strong association? e) a very strong association? a) Which scatterplot shows no association? (2) A. 1 D. 3 C. 2 D. All of these scatterplots (3) E. None of these scatterplots b) Which scatterplot shows a negative association? A Scatterplots I and 3 B. 3 c. Scatterplots 1 and 2 D. Scatterplots 2 and 3 E. 1 OF None of these scatterplots c) Which scatterplot shows a linear association? 5. An online investment blogger advises investing in mutual funds that have performed badly the past year because "regression to the mean tells us that they will do well next year." Is he correct? Choose the correct answer below. A. Yes, he is correct. G. No, he is incorrect. The mutual fund will regress to the mean, but it may not do so for a few years. C. No. he is incorrect. The mutual fund will regress to the mean, but this does not mean it will have a positive return. ID. No, he is incorrect. Although the performance of funds will cluster around the mean on average, he cannot predict how any particular fund will do. 3. A study finds that during blizzards, online sales are highly associated with the number of snow plows on the road; the more plows, the more online purchases. The director of an association of online merchants suggests that the organization should encourage municipalities to send out more plows whenever it snows because, he says, that will increase business. Comment on the director's conclusion. Choose the correct answer below. A. The director is wrong. The lurking variable here is the temperature. A lower temperature leads to a more severe blizzard, which calls for more plows and keeps people at home, where they are more likely to make online purchases. B. The director is wrong. The lurking variable here is the severity of the blizzard. A more severe blizzard calls for more plows and keeps people at home, where they are more likely to make online purchases. C. The director is correct. More plows keep people at home, where they are more likely to make online purchases. D. The director is wrong. If more plows are sent out whenever it snows, the roads will be better and people will leave their home to make purchases, as opposed to staying home and increasing online sales. 4. Is the following statement true or false? If false, explain briefly. Some of the residuals from a least squares linear model will be positive and some will be negative. Choose the correct answer below. A. The statement is true. B. The statement is false because the residuals are all positive. c. The statement is false because there arc some models where the residuals are all negative. D. The statement is false because there are some models where the residuals are all positive. 1. (cont.) c) Does the scatterplot show any outliers? Select the correct choice below and, if necessary. fill in the answer box to complete your choice. No y Yes, the TB drive seems to be overpriced. (Type an integer or a decimal.) C. Yes, the TB drive seems to be underpriced. (Type an integer or a decimal.) 2. Assume that the conditions for correlation are met. Is the following statement true or false? If it is false, explain. Multiplying every value of x by 3 will triple the correlation, Choose the correct answer below. A The statement is false. Multiplying every value of x by 3 does not change the correlation. B. The statement is false. Multiplying every value of y by 3 will triple the correlation. C. The statement is true. Disk drives have been getting larger. Their Capacity (in TB) Price (in $) - capacity is now often given in terabytes (TB) 0.050 30.00 where 1 TB = 1000 gigabytes, or about a 0.140 32.00 trillion bytes. A survey of prices for external 0.210 208.99 disk drives found the data shown to the right. 0.260 46.99 Complete parts a through c. 0.470 72.99 2.0 239.79 3.0 317.00 4.0 440.00 a) Prepare a scatterplot of Price against Capacity. Choose the correct graph below. A B. C. D. 4. 4- 500- 500 = 0- 0- o- o 4 4 500 500 Capacity (in TB) Capacity (in TB) Price un $) Price (in $) b) What can you say about the direction of the association? A. It is positive - It is negative. C It is neither positive nor negative. c) What can you say about the form of the relationship? A It is linear. B. It is curved. COC. There is no pattern. d) What can you say about the strength of the relationship? A. It is weak. It is relatively strong.

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1) Please note the Excel file that I’ve attached – it contains explanations for parts A and B.
A) I’ve produced a scatter plot of the data and it seems to match with answer choice B, please use discretion as the scan is a bit hard to see.
B) I utilized the Excel function, CORREL(array1,array2), to calculate the correlation coefficient of this data set. This coefficient ranges from [-1,+1], where a coefficient: closer to -1 indicates strong negative, closer to 0 has no correlation, and closer to +1 indicates a strong positive. Based on this calculation, we can determine that the direction of the association: A. is positive.
C) Just by looking at the graph we can determine that there is a linear trend to the data relationship, thus A. it is linear.
D) Again, by referring to the correlation coefficient (.929), we can see that there is a strong, positive correlation between capacity and price. So the answer is B. it is relatively strong.
E) An outlier is a data point that strays from the trend shown. For example, for a data set that is primarily linear, any point that is “too high or too low” would be considered an outlier. You can either scan through the data table or scatter plot, either way we know that B. Yes, the .21 TB drive seems to be overpriced. Of course if the price was under the line-of-best-fit, it would be underpriced....

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