1. Fitting a straight line to a set of data yields the following prediction line. Complete (a) through (c) below. V. =3+10X, a. Interpret the meaning of the Y-intercept, b,. Choose the correct answer below. (O A. The Y-intercept, by = 10, implies that when the value of X is 0, the mean value of Y is 10. (O B. The Y-intercept, by, =3, implies that the average value of Y is 3. (O C. The Y-intercept, by =3, implies that when the value of X is 0, the mean value of Y is 3. (O D. The Y-intercept, by = 3, implies that for each increase of 1 unit in X, the value of Y is expected to increase by 3 units. b. Interpret the meaning of the slope, b,. Choose the correct answer below. (O A. The slope, by =10, implies that the average value of Y is 10. (O B. The slope, by =3, implies that for each increase of 1 unit in X, the value of Y is expected to increase by 3 units. (O C. The slope, by =10, implies that for each increase of 1 unitin X, the value of Y is expected to decrease by 10 units. (O D. The slope, by =10, implies that for each increase of 1 unit in X, the value of Y is expected to increase by 10 units. c. Predict the mean value of Y for X =5. ?i = (Simplify your answer.) 2. The production of wine is a multibillion-dollar worldwide industry. In an attempt to develop a model of wine quality as judged by wine experts, data was collected from red wine variants of a certain type of wine. A sample of 12 wines is given. Develop a simple linear regression model to predict wine quality, measured on a scale from 0 (very bad) to 10 (excellent), based on alcohol content (%). Complete parts (a) through (d) below. T Click the icon to view the data of wine quality and alcohol content. a. Construct a scatter plot. Choose the correct graph below. O A. OB Oc. 2 15 e\\ = 40 e\\ = 10 = 3 = = & Rl q g PH q & z ' z z o o w a 3 3 @ D) o D) @ c - - Z 0 E 0 0 40 0 15 0 Alcohol Content (%) Alcohol Content (%) Alcohol 15 Content (%) Wine Quality Rating 0 10 Alcohol Content (%) b. For these data, by =5.1 and b, =0.2. Interpret the meaning of the slope, b, in this problem. Choose the correct answer below. (O A. The slope, by, implies that for each 0.2 percentage decrease in alcohol content, the wine should have an increase in its rating by 1. (O B. The slope, by, implies that the alcohol content is equal to the value of by, in percentages. (O C. The slope, by, implies that for each increase of 1 wine quality rating, the alcohol content is expected to increase by the value of by, in percentages. o P & (O D. The slope, by, implies that for each increase of alcohol percentage of 1.0, the wine quality rating is expected to increase by the value of by. . Predict the mean wine quality for wines with an 10% alcohol content. ?i = (Round to two decimal places as needed.) d. What conclusion can you reach based on the results of (a)-(c)? (O A. Alcohol percentage appears to be affected by the wine quality. Each increase of 1 in quality leads to a mean increase in alcohol of about 0.2. (O B. Alcohol percentage appears to be affected by the wine quality. Each increase of 1 in quality leads to a mean increase in alcohol of about 5.1. (O C. Wine quality appears to be affected by the alcohol percentage. Each increase of 1% in alcohol leads to a mean increase in wine quality of about 0.2 (O D. Wine quality appears to be affected by the alcohol percentage. Each increase of 1% in alcohol leads to a mean increase in wine quality of about 1: Alcohol Content and Quality Rating Wine Alcohol Content (%) Quality Rating o 1 9.5 7 2 10.3 7 3 9.9 7 4 114 9 5 11.2 6 6 11.3 9 7 12.0 8 8 11.8 8 9 119 7 10 12.7 7 11 13.0 9 12 13.3 7 3. Pursuing an MBA is a major personal investment. Tuition and expenses associated with business school programs are costly, but the high costs come with hopes of career advancement and high salaries. A prospective MBA student would like to examine the factors that impact starting salary upon graduation and decides to develop a model that uses program per-year tuition as a predictor of starting salary. Data were collected for 37 full-time MBA programs offered at private universities. The data are stored in the accompanying table. Complete parts (a) through (e) below. 2 Click the icon to view the data on program per-year tuition and mean starting salary. a. Construct a scatter plot. Choose the correct graph below. O > O w O o O o Q & & 200,001 & Q 5 - 5 5 @ 5 @ 3 = t E b E in in 0 200,000 0 80,000 0 200,000 0 80,000 Starting Salary ($) Tuition ($) Starting Salary ($) Tuition ($) b. Assuming a linear relationship, use the least-squares method to determine the regression coefficients by and by . bg = b= (Round the value of by to the nearest integer as needed. Round the value of by to two decimal places as needed.) c. Interpret the meaning of the slope, b, in this problem. Select the correct choice below and fill in the answer box to complete your choice. (Round to the nearest dollar as needed.) O A. The approximate starting salary upon graduation when the tuition is $0 is $ O B. For each increase in tuition of $1 00, the mean starting salary upon graduation is expected to increase by $ O C. For each increase in starting salary upon graduation of $100, the mean tuition is expected to increase by $ O D. The approximate tuition when the mean starting salary is $0 is $ d. Predict the mean starting salary upon graduation for a program that has a per-year tuition cost of $36,833. The predicted mean starting salary will be $ (Round to the nearest dollar as needed.) e. What insights can be obtained about the relationship between program per-year tuition and starting salary upon graduation? (O A. Thereis no relationship between program per-year tuition and mean starting salary upon graduation. (O B. Mean starting salaries upon graduation tend to be higher among programs with higher per-year tuitions. (O C. Having a higher mean starting salary upon graduation results in a lower program per-year tuition. (O D. Mean starting salaries upon graduation tend to be lower among programs with higher per-year tuitions. (O E. Having a higher mean starting salary upon graduation results in a higher program per-year tuition. 2: Tuition vs. Salary Program Per-Year Mean Starting Salary Tuition ($) Upon Graduation ($) 62,381 156,385 67,378 156,496 66,858 144,682 69,021 140,588 66,246 139,548 66,197 156,296 65,831 147,021 69,493 147,346 63,206 136,570 63,280 145,816 67,482 145,487 61,122 148,757 62,028 140,607 58,358 137,295 54,105 125,098 55,165 116,216 56,825 127,918 50,510 130,235 53,248 131,469 49,370 122,594 47,258 112,601 48,576 106,595 49,973 109,797 45,680 111,183 38,930 81,259 47,999 82,361 46,349 103,348 51,120 73,634 36,872 87,653 32,227 74,874 43,168 74,778 41,189 52,674 50,115 62,893 33,748 102,517 24,414 56,991 41,306 77,060 40,408 55,607 o 4. An agent for a residential real estate company in a suburb located outside a major city has the business objective of developing more accurate estimates of the monthly rental cost for apartments. Toward the goal, the agent would like to use the size of an apartment, as defined by square footage to predict the monthly rental cost. The agent selects a sample of 8 one-bedroom apartments and the data are shown. Complete parts (a) through (f). Monthly Rent ($) 900 1,600 850 1,600 2,000 900 1,800 1,400 = Size (Square Feet) 900 1,200 950 1,100 2,000 750 1,250 950 a. Construct a scatter plot. Choose the correct graph below. OA. 2,000 ARent () 0 0 > 2,000 Size (sqft) OB Oc ARent ($) ARent ($) Q 2,000- i' Q 2,000- Q Q ! Q T Q . 7 2 2 2 0 > g 0 > = 0 2,000 0 2,000 Size (Sqft) Size (Sq ft) b. Use the least-squares method to determine the regression coefficients bg and by. Do (Round to one decimal place as needed.) (Round to one decimal place as needed.) c. Interpret the meaning of by and b, in this problem. Choose the correct answer below. (O A. For each increase of 1 square foot in space, the monthly rent is expected to increase by b, dollars. Apartments in this neighborhood cost at least by, dollars. O B. For each increase of 1 square foot in space, the monthly rent is expected to increase by b4 dollars. Since X cannot be zero, by has no practical interpretation. (O C. For each increase of 1 square foot in space, the monthly rent is expected to increase by by dollars. Apartments in this neighborhood cost at least by dollars. (O D. For each increase of 1 square foot in space, the monthly rent is expected to increase by by dollars. Since X cannot be zero, by has no practical interpretation. ob. ARent (5) 2,000~ 0 > 0 2,000 Size (Sqft) Q Q & d. Predict the mean monthly rent for an apartment that has 1,000 square feet. The predicted mean monthly rent for such an apartment is $| (Round to the nearest cent as needed.) e. Why would it not be appropriate to use the model to predict the monthly rent for apartments that have 500 square feet? O A. The model predicts that the monthly rent for an apartment that has 500 square feet would be unrealistically low. (O B. The size of an apartment has no effect on the monthly rent, according to this model. There must be another factor that contributes to the rent price. O . Anapartment with 500 square feet is outside the relevant range for the independent variable. (O D. The correlation between an apartment's size and its monthly rent is too weak to use this model for such a prediction. f. Two people are considering signing a lease for an apartment in this neighborhood. They are trying to decide between two apartments, one with 1,000 square feet for a monthly rent of $1,275 and the other with 1,200 square feet for a monthly rent of $1,425. Based on (a) through (d), which apartment is a better deal? Based on (a) through (d), the apartment with (1) square feet is the better deal. (1) O 1,200 O 1,000 5. Abox office analyst seeks to predict opening weekend box office gross for movies. Toward this goal, the analyst plans to use YouTube trailer views as a predictor. For each of the 65 movies, the YouTube trailer view count, the number of YouTube trailer views from the release of the trailer through the Saturday before a movie opens, and the opening weekend box office grass (in $millions) are collected and stored in the accompanying table. Complete parts (a) through (e) below. 2 Click the icon to view the trailer views and box office gross data. a. Construct a scatter plot. Choose the correct graph below. O o O o O A. O B. Q, Q . o 20 Trailer Views (mil) Trailer Views (mil) o o 0 0 200 0 100 0 100 0 200 Opening Gross ($mil) Trailer Views (mil) Trailer Views (mil) Opening Gross ($mil) . Cpening Gross ($mil) Cpening Gross [($mil) b. Assuming a linear relationship, use the least-squares method to determine the regression coefficients by and b,. by = by= (Round the value of by to two decimal places as needed. Round the value of b, to three decimal places as needed.) . Interpret the meaning of the slope, by, in this problem. Select the correct choice below and fill in the answer box to complete your choice. (Round to three decimal places as needed.) O A The approximate YouTube trailer views when the opening weekend box office gross is $0 is million. O B. For each increase in opening weekend box office gross of $1 million, the number of YouTube trailer views is expected to increase by million. O C. For each increase of 1 million YouTube trailer views, the predicted opening weekend box office gross is expected to increase by $ million. OD. The approximate predicted opening weekend box office gross when the number of YouTube trailer views is 0 is million. d. Predict the mean opening weekend box office gross for a movie that had 34 million YouTube trailer views. The predicted mean opening weekend box office gross will be $ million. (Round to two decimal places as needed.) e. What insights can be obtained about predicting opening weekend box office gross from YouTube trailer views? (O A. As the number of YouTube trailer views increases, the mean opening weekend box office gross can be expected to decrease. (O B. As the number of YouTube trailer views increases, the mean opening weekend box office gross can be expected to increase. (O C. As the mean opening weekend box office increases, the number of YouTube trailer views can be expected to increase. (O D. Asthe mean opening weekend box office increases, the number of YouTube trailer views can be expected to decrease. (O E. There is no relationship between the number of YouTube trailer views and the mean opening weekend box office gross. 3: Trailer Views vs. Opening Weekend Gross Opening Weekend ~ YouTube Trailer Movie Gross ($millions) Views (millions) = The Mummy 32.246 57.897 It Comes At Night 6.001 10.785 Megan Leavey 3.768 10.099 Captain Underpants: The First Epic Movie 23.852 8.725 Wonder Woman 103.251 84.205 Pirates of the Caribbean: Dead Men Tell No Tales ~ 62.983 34.990 Baywatch 18.504 21.764 Everything, Everything 11.727 5.550 Diary of a Wimpy Kid: The Long Haul 7.126 3.836 Alien: Covenant 36.161 45.615 Snatched 19.542 7.791 King Arthur: Legend of the Sword 15.371 28.187 Lowriders 2.404 4.496 Guardians of the Galaxy Vol. 2 146.510 57.324 How to Be a Latin Lover 12.252 7.394 The Circle 9.034 11.145 Sleight 1.702 11.175 Born in China 4.790 0.508 Free Fire 0.994 1.061 Unforgettable 4.785 5.387 The Promise 4.096 6.354 Phoenix Forgotten 1.816 7.714 The Fate of the Furious 98.787 30.870 The Case for Christ 3.968 0.280 Going in Style 11.932 2.645 Smurfs: The Lost Village 13.210 8.124 The Boss Baby 50.199 52.292 The Zookeeper's Wife 3.289 3.886 Ghost in the Shell 18.676 31.055 CHIPS 7.723 7.081 Life 12.502 13.550 Power Rangers 40.300 59.296 Beauty and the Beast 174.751 80.077 The Belko Experiment 4137 5.546 Kong: Skull Island 61.025 35.309 The Shack 16.172 2.532 Logan 88.412 44.196 Before | Fall 4.690 4.989 Get Out Rock Dog Collide The Great Wall Fist Fight A Cure for Wellness John Wick: Chapter 2 The LEGO Batman Movie Fifty Shades Darker Rings The Space Between Us A Dog's Purpose Gold Resident Evil: The Final Chapter Split 20th Century Women xXx: Return of Xander Cage The Founder Monster Trucks Sleepless Patriots Day The Bye Bye Man Live By Night Silence Hidden Figures Underworld: Blood Wars A Monster Calls 33.377 3.705 1.513 18.470 12.202 4.357 30.436 53.003 46.607 13.003 3.776 18.223 3.471 13.602 40.011 1.385 20.130 3.404 10.951 8.344 11.614 13.501 5.106 1.985 22.800 13.689 2.080 6.630 0.942 2.258 11.327 8.966 15177 13.714 31.231 52.612 16.235 6.884 11.698 2.827 23.075 12.606 0.826 27.536 7.273 4.267 3.790 7.597 12.912 7.067 5.020 7.739 16.795 7.643 1. How do you interpret a coefficient of determination, rz, equal to 0.19? Choose the correct answer below. O A. O B. Oc. O D. The interpretation is that 0.81% of the variation in the dependent variable can be explained by the variation in the independent variable. The interpretation is that 81% of the variation in the independent variable can be explained by the variation in the dependent variable. The interpretation is that 19% of the variation in the dependent variable can be explained by the variation in the independent variable. The interpretation is that 0.19% of the variation in the independent variable can be explained by the variation in the dependent variable. If SSR =18 and SSE =12, determine SST, then compute the coefficient of determination, rz, and interpret its meaning. SST= r2= (Type an integer or a decimal. Do not round.) Interpret the meaning of r?. Choose the correct answer below. O A. O B. Oc. MR It means that 1 - r of the variation in the dependent variable cannot be explained by the variation in the independent variable. It means that 1% = 100% of the variation in the dependent variable can be explained by the variation in the independent variable. It means that 12 of the variation in the independent variable can be explained by the variation in the dependent variable. r N L. 3. IfSSR=23and SST= 92, compute the coefficient of determination, r2 and interpret its meaning. 2 - (Type an integer or a decimal. Do not round.) What is the meaning of 22 O A (1 - rz) * 100% of the variation in the independent variable cannot be explained by the variation in the dependent variable. O B. 1-12 of the variation in the dependent variable cannot be explained by the variation in the independent variable. O C. 2 of the variation in the independent variable can be explained by the variation in the dependent variable. O D. 2. 100% of the variation in the dependent variable can be explained by the variation in the independent variable. 4. Inan attempt to develop a model of wine quality as judged by wine experts, data on alcohol content and wine quality was collected from variants of a particular wine. From a sample of 12 wines, a model was created using the percentages of alcohal to predict wine quality. For those data, SSR =19,621 and SST =28,389. Use this information to complete parts (a) through (c) below. a. Determine the coefficient of determination, r2, and interpret its meaning. P = (Round to three decimal places as needed.) Interpret the meaning of . It means that % of the variationin (1) can be explained by the variation in (2) (Round to one decimal place as needed.) b. Determine the standard error of the estimate. Syy = (Round to four decimal places as needed.) c. How useful do you think this regression model is for predicting wine quality? O A. It is very useful for predicting wine quality because the coefficient of determination is close to 0. O B. It is not very useful for predicting wine quality because the coefficient of determination is close to 0. O C. It is very useful for predicting wine quality because the coefficient of determination is close to 1. O D. It is not very useful for predicting wine quality because the coefficient of determination is close to 1. (1) O wine quality (2) O alcohol content. O alcohol content O wine quality. Annual revenues were used to predict the current value of a MLB baseball team, using the accompanying data for a sample of 28 teams. The data are displayed in the accompanying table, and the regression equation and other values are shown below. Use this information to complete parts (a) through (c) below. n n n Y; = - 1041.1088 + 8.5871X;, _ Y, = 43,805, _ Y2 = 82,631,625, _ X;Y, = 14,869,525 i = 1 i = 1 i = 1 Click the icon to view the data table. a. Determine the coefficient of determination, re, and interpret its meaning. 12 = (Round to four decimal places as needed.)What is the meaning of the coefficient of determination? O A. O B. Oc. O D. It measures the variability in the actual franchise value from the predicted waiting times. It is the proportion of the variation in annual revenue that is explained by the variability in franchise value. It is the proportion of the variation in franchise value that is explained by the variability in annual revenue. It measures the variability in the actual annual revenue from the predicted annual revenue. b. Determine the standard error of the estimate. Syx = (Round to four decimal places as needed.) c. How useful do you think this regression model is for predicting the value of a major sports franchise? Since the value of % is (1) theregressionmodel (2)____ for predicting the value of a major sports franchise. 1: Data Table Team Revenue Value Boston 434 2700 Chicago White Sox 269 1350 Cleveland 271 920 Detroit 275 1200 Houston 299 1450 Kansas City 246 950 Los Angeles Angels 350 1750 Minnesota 249 1025 New York Yankees 526 3700 Oakland 216 880 Seattle 289 1400 Tampa Bay 205 825 Texas 298 1550 Arizona 253 1350 Atlanta 275 1500 Chicago Cubs 434 2650 Cincinnati 229 915 Colorado 248 1000 Los Angeles Dodgers 462 2750 Miami 206 940 Milwaukee 239 925 New York Mets 332 2000 Philadelphia 325 1650 Pittsburgh 265 1250 St. Louis 310 1800 San Diego 259 1125 San Francisco 428 2650 Washington 304 1600 1) O equal to O, (2) O is not very useful equal to 1, O should be very useful OO close to 0, O close to 1,6. YouTube trailer views were used to predict movie weekend box office gross. The trailer view and box office gross data are given. A linear regression was performed on these data, and the result is shown. Complete parts (a) through (d). n n n ,= -0.999 +1.4369X, Y Y,=1,500.4410, 3 Y2=106,714.6915, X,=58,843.4842 i=1 =1 =1 2 Click on the icon to view the data table. a. Determine the coefficient of determination, r2, and interpret its meaning. = (Round to three decimal places as needed.) Interpret the meaning of . The value of r* indicates that % of the variationin (1) can be explained by the variationin (2) . (Round to one decimal place as needed.) b. Determine the standard error of the estimate. Syx = (Round to two decimal places as needed.) c. How useful do you think this regression model is for predicting movie weekend box office gross? O A. ltis somewhat useful for predicting box office gross because the coefficient of determination is closer to 1 than it is to 0. (O B. ltis very useful for predicting box office gross because the coefficient of determination is very close to 1. (O C. ltis not useful for predicting box office gross because the coefficient of determination is close to 1. (O D. ltis not useful for predicting box office gross because the coefficient of determination is close to 0. d. Can you think of other variables that might explain the variation in movie weekend box office gross? Select all that apply. [ A. The type of movie might explain the variation in opening weekend box office gross, since some genres are more heavily attended than others. B. The timing of the release of the movie might explain the variation in opening weekend box office gross, because a movie released at the same time as multiple other major movies may get crowded out. . The amount spent on advertising might explain the variation in opening weekend box office gross, because viewers are prabably more likely to watch a movie that has been advertised heavily. 2: Movie Data Opening Weekend YouTube Trailer Movie Gross ($millions) Views (millions) & The Mummy 32.246 57.897 It Comes At Night 6.001 10.785 Megan Leavey 3.768 10.099 Captain Underpants: The First Epic Movie 23.852 8.725 Wonder Woman 103.251 84.205 Pirates of the Caribbean: Dead Men Tell No Tales 62.983 34.990 Baywatch 18.504 21.764 Everything, Everything 11.727 5.550 Diary of a Wimpy Kid: The Long Haul 7.126 3.836 Alien: Covenant 36.161 45.615 Snatched 19.542 7.791 King Arthur: Legend of the Sword 16.371 28.187 Lowriders 2.404 4.496 Guardians of the Galaxy Vol. 2 146.510 57.324 How to Be a Latin Lover 12.252 7.394 The Circle 9.034 11.145 Sleight 1.702 11.175 Born in China 4.790 0.508 Free Fire 0.994 1.061 Unforgettable 4.785 5.387 The Promise Phoenix Forgotten The Fate of the Furious The Case for Christ Going in Style Smurfs: The Lost Village The Zookeeper's Wife Ghost in the Shell CHIPS Life Power Rangers Beauty and the Beast The Belko Experiment Kong: Skull Island The Shack Logan Before | Fall Get Out Rock Dog Collide The Great Wall Fist Fiaht 4.096 1.816 98.787 3.968 11.932 13.210 3.289 18.676 7.723 12.502 40.300 174.751 4137 61.025 16.172 88.412 4.690 33.377 3.705 1.513 18.470 12.202 6.354 7.714 30.870 0.280 2.645 8.124 3.886 31.055 7.081 13.550 59.296 80.077 5.546 35.309 2.532 44.196 4.989 6.630 0.942 2.258 11.327 8.966 A Cure for Wellness John Wick: Chapter 2 The LEGO Batman Movie Fifty Shades Darker Rings The Space Between Us A Dog's Purpose Gold Resident Evil: The Final Chapter Split 20th Century Women xXx: Return of Xander Cage The Founder The Resurrection of Gavin Stone Monster Trucks Sleepless Patriots Day The Bye Bye Man Live By Night Silence Hidden Figures Underworld: Blood Wars A Monster Calls 4.357 30.436 53.003 46.607 13.003 3.776 18.223 3.471 13.602 40.011 1.385 20.130 3.404 1.207 10.951 8.344 11.614 13.501 5.106 1.985 22.800 13.689 2.080 15.177 13.714 31.231 52.612 16.235 6.884 11.698 2.827 23.075 12.606 0.826 27.536 7.273 3.323 4.267 3.790 7.597 12.912 7.067 5.020 7.739 16.795 7.643 (1) O box office gross (2) O YouTube trailer reviews. O YouTube trailer reviews O box office gross