Week 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 Montreal Volume Montreal Price Calgary Volume Calgary Price 58224 2.55 353412 2.34 47699 2.74 264862 2.61 59578 2.39 204975 2.77 61595 2.49 208763 2.70 64889 2.21 326558 2.45 46388 2.75 176891 2.78 38557 2.77 194365 2.77 42141 2.64 203761 2.69 54003 2.52 788517 1.55 42071 2.68 236677 2.54 45460 2.54 212151 2.51 49125 2.50 156506 2.78 35426 2.87 184016 2.84 43584 2.67 194463 2.74 50153 2.60 287830 2.45 46674 2.68 264288 2.69 51860 2.47 252606 2.51 42922 2.66 273315 2.42 49805 2.54 189959 2.58 55995 2.44 210632 2.67 45677 2.54 164154 2.76 44865 2.61 181729 2.67 43586 2.62 277166 2.40 48247 2.61 235714 2.55 35731 2.83 151795 2.84 53838 2.51 177816 2.66 44073 2.69 138010 2.77 37644 2.80 192369 2.71 45730 2.61 176607 2.68 38898 2.74 233628 2.44 38311 2.76 230445 2.66 64728 2.50 210488 2.66 48657 2.72 239181 2.55 40664 2.71 249865 2.41 44247 2.62 303249 2.55 45993 2.58 371406 2.33 56030 2.54 180731 2.65 54484 2.56 194456 2.68 45910 2.45 208841 2.58 48751 2.52 256122 2.53 60742 2.42 193034 2.72 55176 2.46 204850 2.55 55644 2.39 232300 2.61 82453 2.22 287539 2.39 37597 2.68 228471 2.53 36597 2.69 275674 2.40 36801 2.64 201830 2.57 49407 2.45 249857 2.50 54554 2.51 277443 2.56 59472 2.46 212355 2.62 53654 2.48 193319 2.64 50692 2.36 371829 2.22 59119 2.43 376624 2.28 60422 2.48 204535 2.58 46767 2.46 167758 2.85 53102 2.34 359200 2.42 53555 2.50 353337 2.45 48546 2.59 208526 2.74 41009 2.60 134385 2.96 38298 2.60 363914 2.05 48798 2.47 193329 2.76 69101 2.38 224733 2.53 50863 2.47 157224 2.73 47760 2.49 172836 2.72 46896 2.58 230030 2.54 42549 2.64 250358 2.65 52207 2.57 236875 2.63 41088 2.64 165033 2.58 48527 2.60 185174 2.65 46503 2.67 318006 2.35 41118 2.76 262068 2.61 51606 2.60 268585 2.42 62879 2.36 160198 2.78 47687 2.51 160225 2.69 74761 2.31 178346 2.69 69485 2.37 176610 2.72 51770 2.52 153431 2.61 64983 2.46 168018 2.69 43535 2.66 229639 2.39 51743 2.60 205250 2.52 51341 2.59 186280 2.73 50886 2.68 134293 2.87 45651 2.59 301977 2.25 64074 2.45 237514 2.47 64764 2.37 209131 2.53 49457 2.59 167997 2.70 50082 2.65 276670 2.46 52310 2.63 216563 2.53 45751 2.75 217714 2.69 52378 2.52 166223 2.94 58445 2.31 139306 2.99 58358 2.40 208325 2.79 50569 2.50 203041 2.68 53330 2.52 209735 2.70 49580 2.55 231067 2.65 62340 2.53 339476 2.31 48290 2.71 156490 2.78 42684 2.67 196423 2.78 40900 2.74 247229 2.46 45830 2.61 190722 2.84 46650 2.65 277869 2.70 53074 2.60 278231 2.54 61169 2.56 209335 2.69 46265 2.63 339547 2.34 63204 2.53 561446 2.08 85282 2.48 229126 2.63 64041 2.65 258379 2.41 76472 2.49 245116 2.43 81700 2.59 387824 2.37 67928 2.72 226468 2.71 45153 2.89 146194 2.95 45427 2.88 287849 2.09 47658 2.96 190873 2.78 56359 2.73 206240 2.70 66694 2.69 237102 2.56 51112 2.91 379105 1.94 55915 2.79 152468 2.75 47243 2.99 247641 2.68 46638 2.77 199946 2.69 49924 2.71 155152 2.85 52264 2.67 209746 2.58 48975 2.65 199295 2.77 45549 2.63 186959 2.83 46210 2.67 179117 2.67 42410 2.67 197244 2.51 50677 2.62 170395 2.68 50109 2.72 260343 2.57 67832 2.54 216569 2.71 56376 2.72 195231 2.72 37678 3.05 139881 2.96 37749 2.91 114110 3.03 50600 2.88 202566 2.62 64599 2.61 180667 2.78 49489 2.71 197294 2.80 50214 2.68 230029 2.71 50064 2.76 275040 2.54 43033 2.98 225709 2.69 53026 2.66 117891 2.92 44268 2.77 148379 2.93 49738 2.77 223308 2.72 39375 2.75 139748 2.95 56762 2.59 262264 2.40 40729 2.88 216366 2.61 48880 2.76 249485 2.60 40362 2.97 142803 2.97 44836 2.95 154395 2.86 47474 2.83 199287 2.58 66961 2.56 435409 2.25 75783 2.44 204982 2.60 64502 2.64 140170 2.98 59518 2.58 164392 2.87 58238 2.61 127371 2.95 64473 2.75 193649 2.73 72866 2.84 327841 2.40 59073 2.75 208105 2.76 45898 2.77 252685 2.55 Assignment 92 90 72 92 95 94 90 84 89 91 87 96 91 84 44 93 71 89 93 21 68 53 69 92 66 70 81 92 94 63 90 89 83 87 53 90 88 85 90 43 68 89 85 93 91 82 74 87 94 92 96 44 82 93 90 87 89 68 85 85 84 41 79 87 97 89 84 56 83 81 30 51 79 31 83 91 88 78 28 96 45 90 73 81 86 89 64 87 13 65 95 98 85 86 91 76 69 83 93 93 88 42 93 58 87 72 71 81 93 81 28 91 66 74 86 87 62 93 47 96 86 85 82 92 83 81 8 91 79 89 43 97 79 91 73 82 69 35 89 92 87 93 95 86 88 67 70 79 95 87 82 77 53 86 65 68 96 85 91 92 90 81 89 85 82 78 83 88 94 60 88 96 69 95 78 89 85 80 66 79 82 92 76 86 86 74 71 87 83 87 90 41 90 90 35 92 92 11 90 94 Midterm 87 62 75 59 84 85 86 81 54 72 68 82 54 87 61 59 77 75 83 70 86 81 66 84 70 82 58 74 65 50 84 78 68 85 52 60 82 94 45 55 52 74 75 94 84 73 68 85 71 82 75 71 78 81 94 86 91 61 86 73 82 47 61 83 83 89 89 66 86 70 53 70 62 63 83 77 92 82 76 89 73 89 65 80 81 68 73 69 42 68 95 79 68 91 76 62 89 79 84 77 86 72 81 76 82 63 78 91 80 77 43 96 57 50 75 66 62 81 49 87 89 86 69 71 63 88 78 85 85 84 83 77 78 75 67 75 64 74 90 81 80 75 96 60 84 40 49 86 72 83 80 84 88 72 93 79 81 79 82 73 90 53 71 88 67 88 75 83 82 75 64 80 58 66 44 61 80 70 54 91 63 79 59 64 85 70 78 78 58 76 78 66 72 88 60 69 89 59 90 94 FinalExam 88 52 65 68 88 68 82 83 66 76 70 79 45 85 55 41 48 65 82 63 65 70 36 81 40 89 60 87 56 55 70 79 62 81 59 57 83 76 44 54 52 62 63 88 85 63 48 78 64 79 75 53 70 76 95 66 73 45 76 72 84 47 39 85 89 86 69 54 81 75 69 67 47 40 88 69 95 78 64 96 63 72 71 80 82 54 62 77 43 64 85 65 71 91 61 58 79 68 80 75 93 53 90 56 78 61 40 81 75 57 54 90 55 37 72 63 54 53 36 90 84 84 70 63 42 60 69 71 87 72 74 75 70 81 64 77 49 54 86 82 91 74 94 30 76 41 67 73 53 78 82 86 83 76 76 67 78 80 75 71 89 61 51 70 52 73 73 80 85 74 54 75 64 64 51 60 76 73 61 90 54 84 66 66 82 58 64 66 61 77 82 71 74 84 57 59 81 39 84 91 Take Test: Assignment 6 (2015) Multiple Attempts Not allowed. This test can only be taken once. Force Completion This test can be saved and resumed later. Save All Answers Close Window Save and Submit 6 points Question 1 Save Answer Question A - Frozen Pizza This question is adapted from the \"Frozen Pizza\" Mini Case Study Project on page 483 of the textbook. A product manager is interested in learning how sensitive sales are to changes in the unit price of a frozen pizza. For two cities (Montreal and Calgary), data are provided on both Price and Sales volume every four weeks over a period of nearly four years (156 data points). We will examine the relationship between Price and Sales for each of the two cities. The data are in the worksheet FrozenPizza in Asst6_2015_DATA.xlsx. Important instructions: You may use MS Excel for all calculations, including P-values and critical values. Retain all precision throughout by doing your calculations in an MS Excel spreadsheet with cell references instead of retyping numbers. Think about where the data come from. For each city, plot Sales volume versus Price. Then answer these True/False questions for each city: Montreal Calgary The linearity condition is satised. In other words, the relationship is approximately linear. The relationship is positive. There is an obvious high-leverage point. 4 points Question 2 Save Answer Determine the regression equation for each city. What is the estimate of the true regression line for predicting Sales from Price? Montreal: = Calgary: = x + + x (Retain all precision in Excel and report your answers as integers. Be sure to include a minus sign if necessary.) Question 3 10 points Save Answer For each city, test whether Price has statistically signicant ability to explain/predict Sales. Use a 5% signicance level. (Carry all precision in Excel, rather than retyping numbers into your calculator.) Montreal: Ho: 1 0 and Ha: 1 SE(b1) = (Report your answer to two decimal places.) (Report your answer to two decimal places.) Test statistic: t = P-value = 0 (type =, <, >, , , or ) (Report your answer to four decimal places. Type 0.0001 if the P-value is less than this amount.) Calgary: Ho: 1 0 and Ha: 1 SE(b1) = (Report your answer to two decimal places.) (Report your answer to two decimal places.) Test statistic: t = P-value = 0 (type =, <, >, , , or ) (Report your answer to four decimal places. Type 0.0001 if the P-value is less than this amount.) 2 points Question 4 Save Answer For Calgary only, state your conclusion in a properly worded sentence. -- Font family -- -- Font size -- Path: p Words:0 3 points Question 5 Save Answer Some people in the product manager's division suspect that frozen pizza sales are more sensitive to price in one city than in the other. What evidence can you provide to support or refute this claim? In other words, are sales more sensitive to price in one city? Which city? And what is the evidence? -- Font family -- -- Font size -- Path: p Words:0 6 points Question 6 Save Answer For each city, construct a 95% condence interval for the mean Sales if the Price is $2.50. (Round your answers to the nearest integers.) Montreal: Calgary: Question 7 10 points Save Answer Question B - Rating School Performance The Fraser Institute publishes an annual report on school performance in four Canadian provinces. They produce school \"reports cards\" based on objective, publicly available data. A data set was compiled from 85 public secondary schools in the Lower Mainland of British Columbia in 2012. Here is a description of the variables: ESLPct - Percent of students enrolled in English-as-a-Second-Language programs SpecNeedsPct - Percent of special needs students FrenchImmPct - Percent of students in French Immersion programs at the school ParentIncome - Parents' average employment income ($000s) AveExamMark - Average provincial mark (%) of all students in Grades 10, 11, and 12 courses with a mandatory provincial exam. PctExamsFailed - Percent of all mandatory Grades 10, 11, and 12 provincial exams with a failing grade. SchoolExamDiff - The difference between school mark and provincial exam mark in courses with a mandatory provincial exam. A large difference means grades \"ination.\" GraduationRate - Percentage of eligible graduates who graduate in the same school year. DelayedAdvancementRate - Estimated percent of Grade 10 students who will not complete grade 12 within three years. OverallRating - rating on a 0-10 scale, based on standardized scores (which makes it a relative rating). A multiple regression was run with OverallRating as the response variable and 9 explanatory variables. The F statistic reported was 503.40. What are the null and alternative hypotheses for this test statistic? H0: HA: Question 8 Give the degrees of freedom and P-value for the test with F = 503.40. 10 points Save Answer degrees of freedom: and P-value: 2 points 6 points Question 9 Save Answer Save Answer The R2 is 0.984. What does this value tell us? (select the best answer) 98.4% of students don't understand R-squared. 98.4% of the observations are explained by the 9 variables. 98.4% of the observations are explained by OverallRating. 98.4% of the variation in OverallRating is explained by the 9 variables. 98.4% of the variation in the model is explained by OverallRating. Question 10 The table below gives the coefficients for the tted model and the t-statistic for each explanatory variable in the study. Assume all tests are two-sided. Variable Coefficient t-statistic Intercept -2.538 -1.792 ESLPct -0.009 -1.928 SpecNeedsPct 0.003 0.457 FrenchImmPct -0.001 -0.524 ParentIncome ($000) -0.002 -1.808 0.106 7.698 PctExamsFailed -0.085 -6.330 SchoolExamDiff -0.121 -8.644 GraduationRate 0.036 4.110 -0.036 -11.516 AveExamMark DelayedAdvancementRate Fill in the correct choice for each: The hypotheses for each explanatory variable i are H0: The degrees of freedom for the t-statistic are: Thus, values that are less than and HA: . . or greater than will lead to rejection of the null hypothesis. Question 11 3 points Specify which of the following variables is signicantly different from zero in this model. (Select True for signicantly different and False for not signicantly different.) ESLPct Save Answer SpecNeedsPct FrenchImmPct ParentIncome ($000) AveExamMark PctExamsFailed SchoolExamDiff GraduationRate DelayedAdvancementRate 3 points Question 12 Save Answer Thinking about the above question, carefully explain what you conclude when an individual t-statistic is not signicant. -- Font family -- -- Font size -- Path: p Question 13 Words:0 2 points Save Answer Look at the sign in the coefficient for SchoolExamDiff. What does this tell us? (select the best answer) A favourable overall rating arises through a complex interraction of the 9 variables, but the sign of an individual coefficient can't tell us anything. A favourable overall rating arises if a school has a higher school exam differential. Lower ESL percent and lower French immersion percent are correlated with a positive degrees of freedom in the F-statistic, but noninteger (and possibly zero) proportionality in the t-statistic, based on the Central Limit Theorem as applied to the sampling distribution (and adjusted for the pooled test). A favourable overall rating arises if a school has a lower school exam differential. Question 14 3 points Save Answer How would you proceed in order to nd a more parsimonious model that still provides an adequate t to the data? Explain in one or two sentences. -- Font family -- -- Font size -- Path: p Words:0 2 points Question 15 Save Answer Question C - Exam Grades Student stress at nal exam time comes partly from the uncertainty of grades and the consequences of those grades. Can knowledge of a midterm grade be used to predict a nal exam grade? A random sample of 200 BCOM students from recent years was taken and their percentage grades on assignments, midterm exam, and nal exam were recorded. Let's examine the ability of midterm and assignment grades to predict nal exam grades. The data are in the worksheet ExamGrades in the Excel spreadsheet. The three variables are called: Assignment, Midterm, and FinalExam. Fit a regression model to predict FinalExam from Assignment and Midterm. What is the value of R-squared? answer: 4 points 2 points Question 16 Save Answer Save Answer Test the hypothesis that the coefficients for Assignment and Midterm are both zero: Test statistic: Degrees of freedom: P-value: and (Report the P-value to four decimal places.) Question 17 Write a one-sentence conclusion for the previous test. -- Font family -- -- Font size -- Path: p Words:0 4 points 2 points Question 18 Save Answer Save Answer Test the hypothesis that the coefficient for Assignment is zero: Test statistic: Degrees of freedom: P-value: (Report the P-value to four decimal places.) Question 19 Again, write a one-sentence conclusion for the previous test. -- Font family -- -- Font size -- Path: p Question 20 Words:0 4 points Save Answer Create a plot of the distribution of the residuals. Also plot the residuals versus each of the explanatory variables. Then answer the following True/False questions: A histogram of residuals is reasonably close to Normal. Both residual plots look good with basically horizontal bands around the x-axis. Only one of the residual plots looks good. Neither residual plot suggests any issues with the equal spread condition. 4 points Question 21 Save Answer Give an approximate 95% prediction interval for the nal exam grade for a student whose assignment grade is 90% and whose midterm grade is 85%. Approximate 95% PI: (Carry all precision in Excel and then round to one decimal place.) 3 points Question 22 Save Answer Fit a regression model to predict FinalExam using only Midterm. Explain why the coefficient for Midterm and the results of a signicance test for this coefficient differ from what you found with the previous model (with two explanatory variables: Midterm and Assignment). -- Font family -- -- Font size -- Path: p Words:0 19 points Question 23 Save Answer Question 4 - Simple Linear Regression MS Excel Template Below is the template for the output from simple regression using MS Excel. But instead of actual results, the cells are numbered from (1) to (27). Your task is to provide the formulas used to compute each of the cell entries. This question and the next bunch of questions are all about lling in the template. Template with numbered cells: SUMMARY OUTPUT Regression Statistics Multiple R (1) R Square (2) Adjusted R Square (3) Standard Error (4) Observations (5) ANOVA Df SS MS F Signicance F Regression (6) (9) (12) (14) (15) Residual (7) (10) (13) Total (8) (11) Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept (16) (18) (20) (22) (24) (26) X Variable (17) (19) (21) (23) (25) (27) Choose the appropriate formula for each of the drop-down boxes. Note that in some cases a formula may reference another cell using the numbers shown above in the template, e.g., to reference "Observations" it would say "(5)". SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations (1)= (2)= (3) (4)= (5)= ANOVA Df SS MS F (6)= (9)= (12)= (14)= Regression (15) Total Intercept (7)= (10)= (8)= (11)= Coefficients Residual Standard Error (16)= X Variable Question 24 What is the formula for (3)? (1)/(2) r (13)= t Stat P-value Lower 95% Upper 95% (22) (24) (26) (23) (25) (27) 1 points Save Answer (20)= (18) (17)= R2 Signicance F (21)= (19) 1 - (1-R2)[(n-1)/(n-2)] Question 25 1 points Save Answer 1 points Save Answer 1 points Save Answer What is the formula for (15)? Pr[F1,n-2 > (14)] 2Pr[tn-2 > |(20)|] 2Pr[tn-2 > |(21)|] Question 26 What is the formula for (18)? Pr[F1,n-2 > (14)] 2Pr[tn-2 > |(20)|] 2Pr[tn-2 > |(21)|] Question 27 What is the formula for (19)? Pr[F1,n-2 > (14)] 2Pr[tn-2 > |(21)|] 2Pr[tn-2 > |(20)|] Question 28 1 points Save Answer 1 points Save Answer 1 points Save Answer What is the formula for (22)? Pr[F1,n-2 > (14)] 2Pr[tn-2 > |(20)|] 2Pr[tn-2 > |(21)|] Question 29 What is the formula for (23)? 2Pr[tn-2 > |(21)|] Pr[F1,n-2 > (14)] 2Pr[tn-2 > |(20)|] Question 30 What is the formula for (24)? (17) + t*n-2(19) (17) - t*n-2(19) (16) + t*n-2(18) (16) - t*n-2(18) Question 31 1 points Save Answer 1 points Save Answer 1 points Save Answer What is the formula for (25)? (16) - t*n-2(18) (16) + t*n-2(18) (17) + t*n-2(19) (17) - t*n-2(19) Question 32 What is the formula for (26)? (16) + t*n-2(18) (16) - t*n-2(18) (17) + t*n-2(19) (17) - t*n-2(19) Question 33 What is the formula for (27)? (16) + t*n-2(18) (17) + t*n-2(19) (16) - t*n-2(18) (17) - t*n-2(19) 0 points Question 34 Save Answer Have you done all the questions? (there's no pdf for Assignment 6) If so, choose Yes and then submit the assignment before the 1:00pm deadline. (Please make sure you click Save and Submit ; don't rely on the system to submit the assignment for you.) Yes No Save and Submit Click Save and Submit to save and submit. Click Save All Answers to save all answers. Click Close Window to close window. Save All Answers Close Window Save and Submit \f\f