Mrs. Venneman - Home



Scenario 12-2Can we predict annual household electricity costs in a specific region from the number of rooms in the house? Below is a scatterplot of annual electricity costs (in dollars) versus number of rooms for 30 randomly-selected houses in Michigan, along with computer output for linear regression of electricity costs on number of rooms.333375010287000Predictor Coef SE Coef T PConstant 406.9 164.8 2.47 0.020Rooms 58.45 24.77 2.36 0.026S = 246.735 R-Sq = 16.6% R-Sq(adj) = 13.6%1.Use Scenario 12-2. Both the scatterplot and the residual plot indicate that residuals for 3 rooms and 8 and 9 rooms tend to be lower than residuals for 4 through 7 rooms. Which condition for regression inference is not satisfied in this case?a.Mean Annual Electricity costs is a linear function of Number of rooms.b.Observations for each household are independent.c.For each number of rooms, the distribution of annual electricity costs is roughly Normal.d.The standard deviation of annual electricity costs is roughly equal for each number of rooms.e.The data come from a random sample.2.Use Scenario 12-2. Which value in the computer output is the estimate from this sample for the standard deviation of the residuals?a.24.77b.58.45c.164.8d.246.735e.This quantity is not provided by the computer output.3.Use Scenario 12-2. Which of the following statements is a correct interpretation of information in this computer output?a.A one-room house is predicted to have annual electricity costs of $58.45.b.For each additional room a house has, predicted annual electricity costs increase by $58.45.c.For each additional room a house has, predicted annual electricity costs increase by $24.77.d.The standard deviation in annual electrical costs for houses in this sample is $246.735.e.The standard deviation in annual electrical costs for houses in this sample is $24.77.4.Use Scenario 12-2. Assume the conditions for inference have been met. If we test the hypotheses at the ??=?0.05 level. Which of the following is the appropriate conclusion?a.Since the P-value of 0.020 is less than ?, we reject H0. There is convincing evidence of a linear relationship between annual electricity costs and number of rooms.b.Since the P-value of 0.020 is greater than ?, we fail to reject H0. We do not have enough evidence to conclude that there is a linear relationship between annual electricity costs and number of rooms.c.Since the P-value of 0.020 is greater than ?, we accept H0. We have convincing evidence that there is not a linear relationship between annual electricity costs and number of rooms.d.Since the P-value of 0.026 is less than ?, we accept H0. We have convincing evidence that there is not a linear relationship between annual electricity costs and number of rooms.e.Since the P-value of 0.026 is less than ?, we reject H0. We have convincing evidence of a linear relationship between annual electricity costs and number of rooms.Scenario 12-3335280053467000Are high school students who like their English class more likely to enjoy their history class as well? Here is a regression analysis and residual plot for 30 randomly-selected students who were asked to rate how much they liked both English and history on a 0 to 5 scale (a higher rating means the student liked the subject more). [Data from 2004-5 Census at Schools survey in Canada].Predictor Coef SE Coef T PConstant 1.1867 0.5574 2.13 0.042English 0.5254 0.1995 2.63 0.014S = 1.37707 R-Sq = 19.8% R-Sq(adj) = 17.0%5.Use Scenario 12-3. Which of the following conditions for inference does the residual plot suggest has not been satisfied?a.The data come from a random sample.b.Observations for each student are independent.c.The standard deviation of history rating is roughly equal for each value of English rating.d.For each value of English rating, the distribution of history rating is roughly Normal.e.Mean History rating is a linear function of English rating.6.Use Scenario 12-3. Which condition for inference should be checked by examining a Normal Probability plot of the residuals?a.The data come from a random sample.b.Observations for each student are independent.c.The standard deviation of history rating is roughly equal for each value of English rating.d.For each value of English rating, the distribution of history rating is roughly Normal.e.Mean History rating is a linear function of English rating.7.Use Scenario 12-3. Assume (despite the evidence above) that the conditions for inference have been met, and we wish to perform a t-test for regression slope. How many degrees of freedom does the t-statistic’s distribution have?a.2b.28c.29d.30e.588.Use Scenario 12-3. We wish to perform a t-test for regression slope. What is the test statistic for this test?a.0.014b.0.1995c.1.37707d.2.13e.2.639.Use Scenario 12-3. Assuming that the conditions for inference have been met, which of the following represents a 99% confidence interval for the rate of change in history rating for a one-unit change in English rating?a.b.c.d.e.10.Use Scenario 12-3. Which of the following is the estimate from this sample of the standard deviation of the sampling distribution of slopes?a.0.014b.0.042c.0.1995d.0.5574e.1.3770711.Use Scenario 12-3. What does the quantity R-Sq = 19.8% represent?a.The correlation of history rating and English rating—a measure of the strength of the linear relationship between the two variables.b.The average deviation of observed history ratings from the predicted history ratings, expressed as a percentage of the predicted history rating.c.The average deviation of observed English ratings from the predicted English ratings, expressed as a percentage of the predicted English rating.d.The percentage of variation in history rating that can be explained by the regression of history rating on English rating.e.The percentage of variation in English rating that can be explained by the regression of English rating on history rating.12.Use Scenario 12-3. Which of the following is an appropriate conclusion for the test of the hypotheses at the ??=?0.05 level in this context?a.Fail to reject H0: The data provide convincing evidence that there is a linear relationship between English rating and history rating.b.Reject H0. The data provide convincing evidence that there is a linear relationship between English rating and history rating.c.Accept Ha. The data provide convincing evidence that there is a linear relationship between English rating and history rating.d.Reject H0. The data do not provide convincing evidence that there is a linear relationship between English rating and history rating.e.Accept Ha. The data do not provide convincing evidence that there is a linear relationship between English rating and history rating.Scenario 12-5Can we predict annual household electricity costs in a specific region from the number of rooms in the house? Below is computer output for a regression of annual electricity costs (in dollars) on number of rooms for 30 randomly-selected houses in Michigan. Assume the conditions for regression inference have been met.13.Use Scenario 12-5. Based on these data, the margin of error for a 95% confidence interval for the amount of increase in annual electricity costs for a one-room increase in house size is given by:a.24.77b.164.8c.1.96(164.8)d.e.2.048(24.77)14.Use Scenario 12-5. Which of the following represents the proportion of variation in annual electricity costs that is accounted for by the regression of annual electricity costs on number of rooms?a.0.020b.0.026c.0.166d.e.15.Suppose we measure a response variable Y for several values of an explanatory variable X. A scatterplot of log Y versus log X looks approximately like a negatively-sloping straight line. We may conclude thata.the rate of growth of Y is positive, but slowing down over time.b.an exponential growth model would approximately describe the relationship between Y and X.c.a power model would approximately describe the relationship between Y and X.d.the relationship between Y and X is a positively-sloping straight line.e.the residual plot of the regression of log Y on log X would have a “U-shaped” pattern suggesting a non-linear relationship.16.Using least-squares regression on data from 1990 through 2009, I determine that the (base 10) logarithm of the population of a country is approximately described by the equation = –13.5 + 0.01 (Year). Which of the following is the predicted population of the country in the year 2010?a.6.6b.735c.2,000,000d.3,981,072e.33,000,00017.Which of the following would provide evidence that a power law model describes the relationship between a response variable y and an explanatory variable x?a.A normal probability plot of the residuals of the regression of log y versus log x looks approximately linear.b.A normal probability plot of the residuals of the regression of log y versus x looks approximately linear.c.A scatterplot of log y versus x looks approximately linear.d.A scatterplot of y versus log x looks approximately linear.e.A scatterplot of log y versus log x looks approximately linear.Scenario 12-7342900075057000Like most animals, small marine crustaceans are not able to digest all the food they eat. Moreover, the percentage of food eaten that is assimilated (that is, digested) decreases as the amount of food eaten increases. The scatterplot of this relationship for a certain species of crustacean (below) indicates that it is non-linear. However, a scatterplot of ln Assimilation versus ln Food Intake is strongly linear. Below is a computer regression analysis of the transformed data (note that natural logarithms are used).18.Use Scenario 12-7. Which of the following best describe the model that is given by this computer printout?a.A power model with equation = 6.3324 – 0.6513 (ln Food Intake)b.An exponential model with equation = 6.3324 – 0.6513 (ln Food Intake)c.A power model with equation = –0.6513 + 6.3324 (ln Assimilation)d.An exponential model with equation = –0.6513 + 6.3324 (ln Assimilation)e.A power model with equation = –0.6513 + 6.3324 (ln Food Intake)19.Use Scenario 12-7. If, as described above, the scatterplot of ln Assimilation versus ln Food Intake is strongly linear, which of the following best describes the residual plot for the regression of these two variables?a.A roughly straight line.b.A “U-shaped” pattern, with positive residuals for low and high values of food intake and negative residuals in between.c.A “U-shaped” pattern, with negative residuals for low and high values of food intake and positive residuals in between.d.A curved pattern similar to the scatterplot of the variables Food Intake and Assimilation before the logarithmic transformation.e.A random scattering of points on either side of the line whose equation is residuals = 0.Scenario 12-8313372549657000Use of the Internet worldwide increased steadily from 1990 to 2002. A scatterplot of this growth (at right) shows a strongly non-linear pattern. However, a scatterplot of ln Internet Users versus Year is much closer to linear. Below is a computer regression analysis of the transformed data (note that natural logarithms are used).20.Use Scenario 12-8. Which of the following best describe the model that is given by this computer printout?a.A power model with equation = –951.10 + 0.4785 (ln Year)b.A power model with equation = –951.10 + 0.4785 (ln Year) c.A power model with equation = –951.10 + 0.4785 (Year) d.An exponential model with equation = –951.10 + 0.4785 (Year)e.An exponential model with equation = –951.10 + 0.4785 (ln Year) Scenario 12-10223837518923000Use of the internet worldwide increased steadily from 1990 to 2002. A residual plot for the regression of worldwide Internet Users (in millions) on Year is shown below.21.Use Scenario 12-10. Suppose we use the regression whose residuals are shown here to predict the number of Internet users in 1991. Which of the following best describes the accuracy of that prediction?a.The prediction would probably underestimate the true number of Internet users in 1991.b.The prediction would probably overestimate the true number of Internet users in 1991.c.The prediction would probably be accurate.d.We do not have enough information to determine the accuracy of the estimate.e.Since the sample is subject to a random variable, the estimate will underestimate and overestimate with about the same frequency. ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download