2023W2 - Assignment 4_ COMM 191 201 202 2023W2 Application of Statistics in Business

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3/24/24, 10:41 AM 2023W2 - Assignment 4: COMM 191 201 202 2023W2 Application of Statistics in Business https://canvas.ubc.ca/courses/129798/quizzes/676556 1/13 2023W2 - Assignment 4 Due Feb 7 at 11:59p.m. Points 50 Questions 21 Available Jan 31 at 7a.m. - Feb 7 at 11:59p.m. Time Limit None This quiz was locked Feb 7 at 11:59p.m.. Attempt History Attempt Time Score LATEST Attempt 1 5,475 minutes 43 out of 50 Score for this quiz: 43 out of 50 Submitted Feb 6 at 4:35p.m. This attempt took 5,475 minutes.   Question 1 4 / 4 pts Data Spreadsheet for Assignment 4: Assignment_4_Datasets_2023W2.xlsx (https://canvas.ubc.ca/courses/129798/files/30060862? wrap=1) (https://canvas.ubc.ca/courses/129798/files/30060862/download?download_frd=1) Energy Use at YVR Read the Mini Case Study Project on p. 155 of the textbook for background information about energy use at the Vancouver International Airport Authority (YVR). Refer to the Excel data file ( Assignment_4_Datasets_2023W2.xlsx (https://canvas.ubc.ca/courses/129798/files/30060862?wrap=1) (https://canvas.ubc.ca/courses/129798/files/30060862/download?download_frd=1) ). The spreadsheet YVREnergyUse has a portion of the full data set, with the following variables on a monthly basis from January 1997 to December 2010. Date (month and year) Energy Use (thousands of kWh = kilowatt hours) MeanTemp = Mean monthly temperature (degrees Celsius) TotalArea = Total Area of all terminals (sq. m.) Pax_Total = Total passengers (1000s)

3/24/24, 10:41 AM 2023W2 - Assignment 4: COMM 191 201 202 2023W2 Application of Statistics in Business https://canvas.ubc.ca/courses/129798/quizzes/676556 2/13 Correct! An overall upward trend Correct! Some seasonality (e.g., more energy in summer, or more energy in winter) Evidence of lost luggage An overall downward trend Obvious outliers  Question 2 1 / 2 pts Correct! unimodality bimodality Correct! approximate symmetry skewness You Answered outlier(s) variability over time the lack of a time trend  Question 3 2 / 2 pts Create a time plot of Energy Use by Date. Which of the following are clearly visible in this chart? (Select all correct answers) Refer to Exercise 58 in Chapter 3 (p. 114). Examine the two plots. (Note that the second plot is to the right of the first plot at the top of the page.) What features of the data can you see in the histogram that aren’t clear from the time series plot? (Select all correct answers) What features of the data can you see in the time series plot that aren’t clear from the histogram? (Select all correct answers)

3/24/24, 10:41 AM 2023W2 - Assignment 4: COMM 191 201 202 2023W2 Application of Statistics in Business https://canvas.ubc.ca/courses/129798/quizzes/676556 3/13 unimodality bimodality approximate symmetry skewness outlier(s) Correct! variability over time Correct! the lack of a time trend  Question 4 0 / 1 pts You Answered histogram time series plot Correct Answer both are appropriate  Question 5 12 / 12 pts Answer 1: Correct! 0.175 Which graphical display seems more appropriate for these data? Return to the "Energy Use at YVR" study and data set. Create a table of correlations for each pair of variables from: Energy Use, MeanTemp, Total Area, and Pax_Total. Fill in the values below: (Report correlations to exactly three decimal places, e.g., if the value is -0.5 you would type -0.500) Energy MeanTemp TotArea Pax_Total Energy 1 MeanTemp 0.175 1 TotArea 0.863 -0.003 1 Pax_Total 0.449 0.755 0.271 1

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3/24/24, 10:41 AM 2023W2 - Assignment 4: COMM 191 201 202 2023W2 Application of Statistics in Business https://canvas.ubc.ca/courses/129798/quizzes/676556 4/13 Correct! 0.175 Correct Answer .175 Answer 2: Correct! 0.863 Correct! 0.863 Correct Answer .863 Answer 3: Correct! -0.003 Correct! -0.003 Correct Answer -.003 Answer 4: Correct! 0.449 Correct! 0.449 Correct Answer .449 Answer 5: Correct! 0.755 Correct! 0.755 Correct Answer .755 Answer 6: Correct! 0.271 Correct! 0.271 Correct Answer .271  Question 6 1 / 1 pts

3/24/24, 10:41 AM 2023W2 - Assignment 4: COMM 191 201 202 2023W2 Application of Statistics in Business https://canvas.ubc.ca/courses/129798/quizzes/676556 5/13 Correct! 6,260.789 6,260.8 (with margin: 0) Between 6,200 and 6,299  Question 7 1 / 1 pts Correct! 26.2125 26.213 (with margin: 0) Between 26 and 27  Question 8 1 / 1 pts Correct! 0.0307 0.0307 (with margin: 0) Continuing the YVR study, prepare three scatterplots: Energy vs. MeanTemp, Energy vs. TotArea, and Energy vs. Pax_Total. Using Excel, add the regression line and R-square value to each scatterplot. Make sure you read the description of the study in the textbook. That will help you with the next part of this assignment! IMPORTANT: Report each value to EXACTLY four decimal places . e.g. if the value is 0.5 you would type 0.5000. Make sure you include the leading 0 before the decimal point where appropriate. For each scatterplot with regression line, compute and enter the intercept, the slope, and the R-square value (as a proportion, NOT a percentage). You will enter these nine values in the following nine questions (Question 6 through Question 14). (You won't need to submit the scatterplots.) a) Energy vs. MeanTemp: Intercept = Continuing with the previous question, b) Energy vs. MeanTemp: Slope = Continuing with the previous question, c) Energy vs. MeanTemp: R-square =

3/24/24, 10:41 AM 2023W2 - Assignment 4: COMM 191 201 202 2023W2 Application of Statistics in Business https://canvas.ubc.ca/courses/129798/quizzes/676556 6/13 3.07 (with margin: 0) Between 0.03 and 0.04 Between 3 and 4  Question 9 1 / 1 pts Correct! 1,483.4 1,483.4 (with margin: 0) Between 1,400 and 1,499  Question 10 1 / 1 pts Correct! 0.0196 0.0196 (with margin: 0) Between 0.01 and 0.0299  Question 11 1 / 1 pts Correct! 0.7448 0.7448 (with margin: 0) 74.48 (with margin: 0) Between 0.74 and 0.75 Between 74 and 75 Continuing with the previous question, d) Energy vs. TotArea: Intercept = Continuing with the previous question, e) Energy vs. TotArea: Slope = Continuing with the previous question, f) Energy vs. TotArea: R-square =

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3/24/24, 10:41 AM 2023W2 - Assignment 4: COMM 191 201 202 2023W2 Application of Statistics in Business https://canvas.ubc.ca/courses/129798/quizzes/676556 7/13  Question 12 1 / 1 pts Correct! 4,352.5 4,352.5 (with margin: 0) Between 4,300 and 4,400  Question 13 1 / 1 pts Correct! 1.6394 1.6394 (with margin: 0) Between 1.6 and 1.7  Question 14 1 / 1 pts Correct! 0.2016 0.2016 (with margin: 0) 20.16 (with margin: 0) Between 0.2 and 0.21 Between 20 and 21  Question 15 2 / 2 pts Continuing with the previous question, g) Energy vs. Pax_Total: Intercept = Continuing with the previous question, h) Energy vs. Pax_Total: Slope = Continuing with the previous question, i) Energy vs. Pax_Total: R-square =

3/24/24, 10:41 AM 2023W2 - Assignment 4: COMM 191 201 202 2023W2 Application of Statistics in Business https://canvas.ubc.ca/courses/129798/quizzes/676556 8/13 Correct! TotArea MeanTemp Pax_Total All three are equally good predictors  Question 16 6 / 6 pts Continuing with the previous question, which variable provides the best prediction of Energy Use? Use the appropriate quantities you computed in the set of questions above as the indicator of "best prediction." More on Interpreting Correlation Simpson’s Paradox can occur in regression, when a relationship between variables within groups of observations is reversed if all the data are combined. Here is an example: Group X Y Group X Y 1 1 10.2 2 6 18.6 1 2 8.8 2 7 16.9 1 3 8.9 2 8 16.2 1 4 6.8 2 9 15.3 1 5 5.9 2 10 13.7 Make a scatterplot of the data for Group 1 and add the least squares line. What is the correlation for Group 1? Answer: -0.965 Add the data for Group 2 to your scatterplot along with the least squares line. What is the correlation for Group 2? Answer: -0.989 Now add the least squares line for the dataset with all 10 observations to your plot. What is the correlation for this combined data?

3/24/24, 10:41 AM 2023W2 - Assignment 4: COMM 191 201 202 2023W2 Application of Statistics in Business https://canvas.ubc.ca/courses/129798/quizzes/676556 9/13 Answer 1: Correct! -0.965 Correct! -0.965 Correct Answer -.965 Correct Answer -0.96 Correct Answer -.96 Correct Answer -0.97 Correct Answer -.97 Answer 2: Correct! -0.989 Correct! -0.989 Correct Answer -.989 Correct Answer -0.98 Correct Answer -.98 Correct Answer -0.99 Correct Answer 0.99 Answer: 0.631 (Report your answers to exactly THREE decimal places, with a leading 0; e.g., -0.290) Note: You will need the scatterplots to answer the next question. Hint for scatterplot of Groups 1 and 2: Put the X values in one column, the Group 1 and 2 values in the next column, the Group 1 values (again) in the third column, and the Group 2 values (again) in the fourth column. Excel can then build the plot with 1 X variable and three Y variables, and it will be able to give you a regression line for each of the three possibilities.

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3/24/24, 10:41 AM 2023W2 - Assignment 4: COMM 191 201 202 2023W2 Application of Statistics in Business https://canvas.ubc.ca/courses/129798/quizzes/676556 10/13 Answer 3: Correct! 0.631 Correct! 0.631 Correct Answer .631 Correct Answer 0.63 Correct Answer .63  Question 17 3 / 3 pts Answer 1: A line with negative slope and an intercept around 0. A line with negative slope and an intercept around 25 Correct! A line with negative slope and an intercept around 11. A line with positive slope and an intercept around 11. A line with positive slope and an intercept around 7. Answer 2: A line with negative slope and an intercept around 0. Correct! A line with negative slope and an intercept around 25 A line with negative slope and an intercept around 11. A line with positive slope and an intercept around 11. A line with positive slope and an intercept around 7. Answer 3: A line with negative slope and an intercept around 0. A line with negative slope and an intercept around 25 A line with negative slope and an intercept around 11. Match the Group from the previous question with the best description of its least squares line. Group 1 → A line with negative slope and an intercept around 11. Group 2 → A line with negative slope and an intercept around 25 Groups 1 and 2 combined → A line with positive slope and an intercept around 7.

3/24/24, 10:41 AM 2023W2 - Assignment 4: COMM 191 201 202 2023W2 Application of Statistics in Business https://canvas.ubc.ca/courses/129798/quizzes/676556 11/13 A line with positive slope and an intercept around 11. Correct! A line with positive slope and an intercept around 7.  Question 18 2 / 2 pts Negative association, no pattern, not much spread. Negative association, nonlinear form, not much spread, no outliers. Correct! Negative association, linear form, not much spread, no outliers. No association, possibly linear form, some spread. Negative association, curved form, lots of spread, possibly a couple outliers.  Between 1980 and 2005, average mortgage interest rates in the U.S. fluctuated from a low of under 6% to a high of over 14%. Is there a relationship between the amount of money people borrow and the interest rate that’s offered? Here is a scatterplot of Total Mortgages in the U.S. (in millions of 2005 dollars) vs. Interest Rates at various times over the past 26 years. The correlation is -0.84. Which statement best describes the relationship between Total Mortgages and Interest Rate ? (Select the best answer)

3/24/24, 10:41 AM 2023W2 - Assignment 4: COMM 191 201 202 2023W2 Application of Statistics in Business https://canvas.ubc.ca/courses/129798/quizzes/676556 12/13 Question 19 2 / 4 pts Answer 1: You Answered 0 Correct Answer -0.84 Correct Answer -.84 Answer 2: Correct! -0.84 Correct! -0.84 Correct Answer -.84  Question 20 0 / 2 pts Correct Answer It would move toward 0. It would move toward -1. You Answered It would move toward +1. It would stay the same. If we standardized both variables (i.e., turned them into z-scores) in the previous question, what would the correlation coefficient between the standardized variables be? NOTE: Data are not needed to answer this. Just think about the properties of the correlation coefficient. Answer: 0 If we were to measure Total Mortgages in thousands of dollars instead of millions of dollars, what would the correlation coefficient become? NOTE: Data are not needed here either! Answer: -0.84 (Report your answers to TWO decimal places, with the leading 0; e.g., -0.20) Suppose in another year, interest rates were 11%, and mortgages totalled $250 million. How would including that year with these data affect the correlation coefficient?

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3/24/24, 10:41 AM 2023W2 - Assignment 4: COMM 191 201 202 2023W2 Application of Statistics in Business https://canvas.ubc.ca/courses/129798/quizzes/676556 13/13 There's not enough information to answer this question.  Question 21 0 / 1 pts Yes. The correlation is strongly negative. Yes. There is a clear causal link between mortgage rates and more mortgages. Correct Answer No. We don’t know why lower rates are associated with more mortgages; there may be other economic factors. You Answered No. While there is a strong negative correlation, it is not evidence of an association. No. The correlation is reversed; if people take out more mortgages, the mortgage rates will be lowered. Quiz Score: 43 out of 50 Do these data provide proof that if mortgage interest rates are lowered, people will take out more mortgages?

2023W2 - Assignment 4_ COMM 191 201 202 2023W2 Application of Statistics in Business

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