Consumption (thousands of dollars) Income (thousands of dollars) 20 18 18 13 27 21 36 27 37 26 45 36 50 39 a) With the help of your graphing calculator, make a scatter plot and decide whether a linear model is appropriate. Carefully draw the scatter plot on your papers, as well.
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- Briefly describe the concept of VIF (what is it, why do we use it) and explain how to calculate VIF in a model with 3 independent variables.Mark Gershon, owner of a musical instrument distributorship, thinks that demand for guitars may be related to the number of television appearances by the popular group Maroon 5 during the previous month. Gershon has collected the data shown in the following table: Maroon 5 TV Appearances Demand for Guitars This exercise contains only part a. a) Graph these data using the point drawing tool. The plotted graph shows a pattern that can be described by: A. Seasonality C. Random variations 3 5 8 7 7 79 3 5 6 6 10 7 B. Trend O D. Cycles 12- 11- 10- 9- 8- 7- 6- 5- 4- 3- 2- 1- 0- Guitar Demand 4 TV Appearances -00 10 11What type pf correlation does the graph show ?
- Mark Gershon, owner of a musical instrument distributorship, thinks that demand for guitars may be related to the number of television appearances by the popular group Maroon 5 during the previous month. Gershon has collected the data shown in the following table: Maroon 5 TV Appearances Demand for Guitars This exercise contains only part a. a) Graph these data using the point drawing tool. The plotted graph shows a pattern that can be described by: A. Seasonality C. Random variations 3 5 8 7 7 70 3 5 6 6 10 7 B. Trend D. Cycles C 12- 11- 10- 9. 8- 7- 6- 5- 4- 3- 2- 1- 0- 0 Guitar Demand 1 2 3 5 4 TV Appearances 8 9 10 117. Dependent & independent variables; positive & inverse relationships: Ypsilanti Market Research conducted a survey to find out whether people who earn more money purchase more expensive goods. The following table indicates the relationship between income the survey subjects earned and the price of the car that they purchased. Price Income (Thousands of dollars per car) (Thousands of dollars per year) 0. 10 20 15 40 20 60 25 80 30 100 In the diagram below, draw the graph corresponding to the above table.1. Solve the following problem by using Excel for graph sketching. A soda vendor at Louisiana State University football games observes that more sodas are sold the warmer the temperature at game time is. Based on 32 home games covering five years, the vendor estimates the relationship between soda sales and temperature to be y = -240 + 8x, where y = the number of sodas she sells and .x = temperature in degrees Fahrenheit, (a) Interpret the estimated slope and intercept. Do the estimates make sense? Why, or why not? (b) On a day when the temperature at game time is forecast to be 80°F, predict how many sodas the vendor will sell. (c) Below what temperature are the predicted sales zero? (d) Sketch a graph of the estimated regression line.
- The table lists weights (pounds) and highway mileage amounts (mpg) for seven automobiles. Use the sample data to construct a scatterplot. Use the first variable for the x-axis. Based on the scatterplot, what do you conclude about a linear correlation? Weight (lb) Highway (mpg) Which scatterplot below shows the data? O A. 40- 20+ 2000 5000 2855 3050 3810 3985 4250 2275 3525 33 32 27 24 22 39 28 Weight (lb) Q Q O B. 40 20+ 2000 AHH 5000 Weight (lb) Q Q Is there a linear relationship between weight and highway mileage? O A. No, there appears to be a relationship, but it is not linear. O B. Yes, as the weight increases the highway mileage decreases. O C. Yes, as the weight increases the highway mileage increases. OD. No there appears to be no relationshin C O C. Q 40- M Q 20++ 2000 5000 Weight (lb) Highway ( O D. Highway (mpg) 40- 20+ 2000 5000 Weight (lb) Q← Café Michigan's manager, Gary Stark, suspects that demand for mocha latte coffees depends on the price being charged. Based on historical observations, Gary has gathered the following data, which show the numbers of these coffees sold over six different price values: Price $2.50 $3.50 $1.90 $4.20 $3.20 $4.10 Number Sold 760 515 980 250 320 490 D Using simple linear regression and given that the price per cup is $1.75, the forecasted demand for mocha latte coffees will be 1862.8 cups (enter your response rounded to one decimal place). 88Construct a table from the data shown on the graph below. Which is the dependent variable and which the independent variable? Summarize the data in equation form.
- Given the following data X (consumers of teff) or popn 3 6 8 1 13 13 14 Y ( teff consumption) 8 6 10 12 12 14 20 year 2013 2014 2015 2016 2017 2018 2019 Estimate the regression equation, Y= a+bX, Where Y denotes demand for teff while X is consumers of teff (population) By assuming demand for teff is only affected by its consumers, find the amount demand for teff in the year 2022 if the populations (consumers of teff) are about 18 people? (Hint: use the least square method, parameter a and b can be estimated by solving the two linear equations) SY= na+ bSX SXY=aSX +b Where n is number of years. For example, Estimate the sales for 2012, 2015 and fit a linear regression equation and draw a trend line.ar X Sales (Y) XY X2 year X Sales (Y) XY X2 2002 1 22734 22734 1 2003 2 24731 49462 4 2004 3 31489 94467 9 2005 4 44685 178740 16 2006 5 55319…3. Boyoung is writing a paper about the effect of Sunday liquor sales on drunk driving. She has panel data on which states allow liquor to be sold on Sunday in which years and wishes to estimate a difference-in-differences model. She writes the following regression equation: Year DUIRate;; = atate +a? + BTreatmentt +yControl;t + Eit i Which of the following changes does Boyoung need to make? a) She should include a constant in the regression equation. b) She should not include controls because they're already accounted for by fixed effects. c) She should include a time trend instead of time-fixed effects. d) None of the above are changes she needs to make.A kids' organization sold 570 bars last year at $ 2.55 per candy bar. Research has suggested that for each $ 0.25 price increase, they will sell 20 less candy bars. They want to know what price should they sell their candy bars at to maximize their revenue. Please help them out, showing your work neatly in the following steps. And please label the steps clearly with the letters A through F A) Define your variables. This means that for every letter you use to represent a value, you communicate what it equals in words. B) Find the linear equation that relates the price and the number sold. C) Determine a function that represents the Revenue. (Remember, Revenue = (Price)*(Number Sold)). D) Graph your revenue function on your calculator or Desmos or something similar and on your paper, labeling the axes and the maximum point. E) Uusing your calculator or Desmos or something similar, use your graph to determine the price that maximizes the revenue for the organization. Do NOT use calculus…
