MATH302 D011 Fall 2023 - APEI

1/17/24, 3:29 PM William Bridgeforth - MATH302 D011 Fall 2023 - APEI https://myclassroom.apus.edu/d2l/lms/quizzing/user/quiz_submissions_attempt.d2l?isprv=&qi=270932&ai=3068927&isInPopup=0&cfql=0&fromQB=… 1/24 Week 7 Knowledge Check Homework Practice Questio… Attempt 1 of 4 Written Jan 17, 2024 3:07 PM - Jan 17, 2024 3:56 PM Attempt Score 17 / 20 - 85 % Overall Grade (Highest Attempt) 17 / 20 - 85 % Question 1 1 / 1 point A vacation resort rents SCUBA equipment to certified divers. The resort charges an up-front fee of $25 and another fee of $12.50 an hour. What is the independent variable? Hide ques±on 1 feedback fee amount driver certification time resort location The equation is Dollars = $12.5(hour) + $25 Dollars depends on how many hours you use the equipment for. Dollars is the dependent variable and time (in hours) is the independent variable.

1/17/24, 3:29 PM William Bridgeforth - MATH302 D011 Fall 2023 - APEI https://myclassroom.apus.edu/d2l/lms/quizzing/user/quiz_submissions_attempt.d2l?isprv=&qi=270932&ai=3068927&isInPopup=0&cfql=0&fromQB=… 2/24 Question 2 1 / 1 point Which of the following equations are linear? Hide ques±on 2 feedback Question 3 1 / 1 point You move out into the country and you notice every Spring there are more and more Deer Fawns that appear. You decide to try and predict how many Fawns there will be for the up coming Spring. You collect data to, to help estimate Fawn Count for the upcoming Spring season. You collect data on over the past 10 years. x1 = Adult Deer Count x2 = Annual Rain in Inches x3 = Winter Severity Where Winter Severity Index: 1 = Warm 2 = Mild 3 = Cold 8x 3 +4y 2 y=6x+8 3y=6x+5y 2 y-x=8x 2 A linear equation is a linear line. If a problem has a squared or a cubed term, it isn't linear. It is a quadratic equation.

1/17/24, 3:29 PM William Bridgeforth - MATH302 D011 Fall 2023 - APEI https://myclassroom.apus.edu/d2l/lms/quizzing/user/quiz_submissions_attempt.d2l?isprv=&qi=270932&ai=3068927&isInPopup=0&cfql=0&fromQB=… 4/24 Question 4 1 / 1 point You are thinking about opening up a Starbucks in your area but what to know if it is a good investment. How much money do Starbucks actually make in a year? You collect data to, to help estimate Annual Net Sales, in thousands, of dollars to know how much money you will be making. You collect data on 27 stores to help make your decision. x1 = Rent in Thousand per month x2 = Amount spent on Inventory in Thousand per month x3 = Amount spent on Advertising in Thousand per month R-squared: 97.74% of variation in Fawn Count is accounted for by Adult Count, Annual Rain in inches and Winter Severity in this model. If you want to give a more conservative estimate, you can use the Adjusted R- squared. This can make sure you don't over promise on what the model can do. But the interpretations are the same. Adjusted R-squared: 96.61% of variation in Fawn Count is accounted for by Adult Count, Annual Rain in inches and Winter Severity in this model. Note: Correlation is a value between -1 and 1. This STAYS a decimal. R-square gets converted from a decimal to a percentage. The Correlation IS NOT a percent, leave it as a decimal. Note: Correlation is a value between -1 and 1. This STAYS a decimal. R-square gets converted from a decimal to a percentage. The Correlation IS NOT a percent, leave it as a decimal.

1/17/24, 3:29 PM William Bridgeforth - MATH302 D011 Fall 2023 - APEI https://myclassroom.apus.edu/d2l/lms/quizzing/user/quiz_submissions_attempt.d2l?isprv=&qi=270932&ai=3068927&isInPopup=0&cfql=0&fromQB=… 5/24 x4 = Sales in Thousand per month x5= How many Competitors stores are in the Area Find the estimated regression equation which can be used to estimate Annual Net Sales when using these 5 variables are predictor variables. See Attached Excel for Data. Starbuck Sales data.xlsx Hide ques±on 4 feedback Annual Net Sales = -49.0449 + 0.9911(Rent) + 0.9823(Inventory) + 0.9782(Advertising) + 27.6181(Sales) - 2.9766(Competitor) Annual Net Sales = -49.0449 + 15.1571(Rent) + 0.1744(Inventory) + 12.1779(Advertising) + 14.2972(Sales) - 2.9766(Competitor) Annual Net Sales = 44.4256 + 5.5406(Rent) + 0.0979(Inventory) + 3.7165(Advertising) + 2.9543(Sales) - 2.5614(Competitor) Annual Net Sales = -1.1039+ 2.736(Rent) + 1.9204(Inventory) + 3.2767(Advertising) + 4.8384(Sales) - 1.1620(Competitor) You can run a Multiple Linear Regression in Excel using the Data Analysis ToolPak. Data -> Data Analysis -> Scroll to Regression Highlight Annual Net Sales for the Y Input: Highlight all 5 columns from Rent to Competitor for the X Input: Make sure you click on Labels and Click OK If done correctly then you look under the Coefficients for the values to write out the Regression Equation

1/17/24, 3:29 PM William Bridgeforth - MATH302 D011 Fall 2023 - APEI https://myclassroom.apus.edu/d2l/lms/quizzing/user/quiz_submissions_attempt.d2l?isprv=&qi=270932&ai=3068927&isInPopup=0&cfql=0&fromQB=… 7/24 Starbuck Sales data.xlsx Hide ques±on 5 feedback 98.24% of variation in the Annual Net Sales is accounted for by Rent, Inventory, Advertising, Sales per Month and # of Competitor store in this model. 99.11% of variation in the Annual Net Sales is accounted for by Rent, Inventory, Advertising, Sales per Month and # of Competitor store in this model. 27.62% of variation in the Annual Net Sales is accounted for by Rent, Inventory, Advertising, Sales per Month and # of Competitor store in this model. 99.25% of variation in the Annual Net Sales is accounted for by Rent, Inventory, Advertising, Sales per Month and # of Competitor store in this model. The R-squared value is the amount of explained variance in the data points in the model. You convert this decimal to a percent. You can run a Multiple Linear Regression in Excel using the Data Analysis ToolPak. Data -> Data Analysis -> Scroll to Regression Highlight Annual Net Sales for the Y Input: Highlight all 5 columns from Rent to Competitor for the X Input: Make sure you click on Labels and Click OK If done correctly then R Square 0.982353754 Adjusted R Square 0.978152267 R-squared:

1/17/24, 3:29 PM William Bridgeforth - MATH302 D011 Fall 2023 - APEI https://myclassroom.apus.edu/d2l/lms/quizzing/user/quiz_submissions_attempt.d2l?isprv=&qi=270932&ai=3068927&isInPopup=0&cfql=0&fromQB=… 8/24 Question 6 1 / 1 point You move out into the country and you notice every Spring there are more and more Deer Fawns that appear. You decide to try and predict how many Fawns there will be for the up coming Spring. You collect data to, to help estimate Fawn Count for the upcoming Spring season. You collect data on over the past 10 years. x1 = Adult Deer Count x2 = Annual Rain in Inches x3 = Winter Severity Where Winter Severity Index: 1 = Warm 2 = Mild 3 = Cold 98.24% of variation in the Annual Net Sales is accounted for by Rent, Inventory, Advertising, Sales per Month and # of Competitor store in this model. If you want to give a more conservative estimate, you can use the Adjusted R- squared. This can make sure you don't over promise on what the model can do. But the interpretations are the same. Adjusted R-squared: 97.82% of variation in the Annual Net Sales is accounted for by Rent, Inventory, Advertising, Sales per Month and # of Competitor store in this model. Note: Correlation is a value between -1 and 1. This STAYS a decimal. R-square gets converted from a decimal to a percentage. The Correlation IS NOT a percent, leave it as a decimal.

1/17/24, 3:29 PM William Bridgeforth - MATH302 D011 Fall 2023 - APEI https://myclassroom.apus.edu/d2l/lms/quizzing/user/quiz_submissions_attempt.d2l?isprv=&qi=270932&ai=3068927&isInPopup=0&cfql=0&fromQB… 10/24 Question 7 0 / 1 point Which residual plot has the best linear regression model? Winter Severity 0.249286765 Fawn Count = -5.5591 + 0.3071(Adult Count) + 0.3978(Annual Rain) + 0.2493(Winter Severity) Plug in, Adult Deer Count = 10, Annual Rain = 13.5 and Winter Severity = 4 Fawn Count = -5.5591 + 0.3071(10) + 0.3978(13.5) + 0.2493(4) a b c d e f

1/17/24, 3:29 PM William Bridgeforth - MATH302 D011 Fall 2023 - APEI https://myclassroom.apus.edu/d2l/lms/quizzing/user/quiz_submissions_attempt.d2l?isprv=&qi=270932&ai=3068927&isInPopup=0&cfql=0&fromQB… 11/24 Hide ques±on 7 feedback Question 8 1 / 1 point In the context of regression analysis, what is the definition of an influential point? Question 9 1 / 1 point You determine there is a strong linear relationship between two variables using a test for linear regression. Can you immediately claim that one variable is causing the second variable to act in a certain way? Hide ques±on 9 feedback A good residual plot has an even distribution of data points above and below the line x = 0. Observed data points that are far from the least squares line Observed data points that are far from the other observed data points in the horizontal direction Observed data points that are close to the least squares line Observed data points that are close to the other observed data points in the horizontal direction No, you should examine the situation to identify lurking variables that may be influencing both variables. No, the correlation would need to be a perfect linear relationship to be sure. No, you must first decide if the relationship is positive or negative. Yes, a strong linear relationship implies causation between the two variables. No, correlation does not equal causation.

1/17/24, 3:29 PM William Bridgeforth - MATH302 D011 Fall 2023 - APEI https://myclassroom.apus.edu/d2l/lms/quizzing/user/quiz_submissions_attempt.d2l?isprv=&qi=270932&ai=3068927&isInPopup=0&cfql=0&fromQB… 13/24 If there are 15 data points in a set of data, what is the number of degree of freedom for the Residual? Hide ques±on 12 feedback Question 13 1 / 1 point It has long been thought that the length of one's femur is positively correlated to the length of one's tibia. The following are data for a classroom of students who measured each (approximately) in inches. Femur Length Tibia Length 18.7 14.2 20.5 15.9 16.2 13.1 15.0 12.4 19.0 16.2 21.3 15.8 21.0 16.2 15 13 14 12 The Residuals have n -2 degrees of freedom. 15 - 2 = 13

1/17/24, 3:29 PM William Bridgeforth - MATH302 D011 Fall 2023 - APEI https://myclassroom.apus.edu/d2l/lms/quizzing/user/quiz_submissions_attempt.d2l?isprv=&qi=270932&ai=3068927&isInPopup=0&cfql=0&fromQB… 14/24 14.3 12.1 15.8 13.0 18.8 14.3 18.7 13.8 Regression Statistics Multiple R 0.9305 R Square 0.8659 Adjusted R Square 0.8510 Standard Error 0.5963 Observations 11 ANOVA df SS MS F Significance F Regression 1 20.6611 20.6611 58.0968 3.25116E-05 Residual 9 3.2007 0.3556 Total 10 23.8618

1/17/24, 3:29 PM William Bridgeforth - MATH302 D011 Fall 2023 - APEI https://myclassroom.apus.edu/d2l/lms/quizzing/user/quiz_submissions_attempt.d2l?isprv=&qi=270932&ai=3068927&isInPopup=0&cfql=0&fromQB… 16/24 Model Summary b Model R R Square Adjusted R Square Std. Error of the Estimate 1 .734 a .539 .525 4.01409 a. Predictors: (Constant), Wrist Circumference b. Dependent Variable: Height ANOVA a Model Sum of Squares df Mean Square F Sig. 1 Regression 621.793 1 621.793 38.590 .000 b Residual 531.726 33 16.113 Total 1153.519 34 a. Dependent Variable: Height b. Predictors: (Constant), Wrist Circumference Model Unstandardized Coefficients Standardized Coefficients t Sig. B Std. Error Beta 1 (Constant) 38.177 5.089 7.502 .000 Wrist Circumference 4.436 .714 .734 6.212 .000 What is the value of the test statistic to see if the correlation is statistically significant? 0.539 7.502 4.436 5.089 6.212

1/17/24, 3:29 PM William Bridgeforth - MATH302 D011 Fall 2023 - APEI https://myclassroom.apus.edu/d2l/lms/quizzing/user/quiz_submissions_attempt.d2l?isprv=&qi=270932&ai=3068927&isInPopup=0&cfql=0&fromQB… 17/24 Hide ques±on 14 feedback Question 15 1 / 1 point Body frame size is determined by a person's wrist circumference in relation to height. A researcher measures the wrist circumference and height of a random sample of individuals. Model Summary b Model R R Square Adjusted R Square Std. Error of the Estimate 1 .734 a .539 .525 4.01409 a. Predictors: (Constant), Wrist Circumference b. Dependent Variable: Height ANOVA a Model Sum of Squares df Mean Square F Sig. 0.734 You need to test the slope. The T-stat that corresponds with the slope (or Wrist Circumference) is 6.212

1/17/24, 3:29 PM William Bridgeforth - MATH302 D011 Fall 2023 - APEI https://myclassroom.apus.edu/d2l/lms/quizzing/user/quiz_submissions_attempt.d2l?isprv=&qi=270932&ai=3068927&isInPopup=0&cfql=0&fromQB… 19/24 Question 17 1 / 1 point Bone mineral density and cola consumption has been recorded for a sample of patients. Let x represent the number of colas consumed per week and y the bone mineral density in grams per cubic centimeter. Assume the data is normally distributed. Calculate the correlation coefficient using technology (you can copy and paste the data into Excel). Round answer to 4 decimal places. Make sure you put the 0 in front of the decimal. x y 1 0.883 2 0.8734 3 0.8898 4 0.8852 5 0.8816 6 0.863 7 0.8634 8 0.8648 9 0.8552 10 0.8546 11 0.862 Answer:___ Answer: -0.8241 Hide ques±on 17 feedback Question 18 1 / 1 point Use =CORREL function in Excel.

1/17/24, 3:29 PM William Bridgeforth - MATH302 D011 Fall 2023 - APEI https://myclassroom.apus.edu/d2l/lms/quizzing/user/quiz_submissions_attempt.d2l?isprv=&qi=270932&ai=3068927&isInPopup=0&cfql=0&fromQB… 20/24 A teacher believes that the third homework assignment is a key predictor in how well students will do on the midterm. Let x represent the third homework score and y the midterm exam score. A random sample of last terms students were selected and their grades are shown below. Assume scores are normally distributed. Calculate the correlation coefficient using technology (you can copy and paste the data into Excel). Round answer to 4 decimal places. Make sure you put the 0 in front of the decimal. HW3 Midterm 13.1 59.811 21.9 87.539 8.8 53.728 24.3 95.283 5.4 39.174 13.2 66.092 20.9 89.729 18.5 78.985 20 86.2 15.4 73.274 25 93.25 9.7 52.257 6.4 43.984 20.2 79.762 21.8 84.258 23.1 92.911 22 87.82 11.4 54.034 14.9 71.869 18.4 76.704 15.1 70.431