b. Best Definition (Make sure to supplement your answers with the relevant graph): (5 points) Given the following univariate regression: Y₁ = ß₁ + Â₂ס + Û₁ Prove that ẞ2 is the best (15 points) 1. Define and mathematically prove the following statistical concepts a. Unbiased aluguend Definition (Make sure to supplement your answers with the relevant graph): ASOS aninge (5 points) эшви odmusbo Iwer bac garbanove oil glad con of complaisas svig antisa i Tari contis I scombueno que seu jod orabo gru Given the following univariate regression: Y₁ = Â₁ + Â₂ס + û₁ Prove that E(B2) = B₂ (10 points) Il mexa of 208
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- 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…In the Managerial Solution, we estimated a focus group's demand curve for iTunes downloads. The estimated coefficient on price was-413, and the 1-statistic was -12.8. nage d coe ndard Using these values, what is the standard error of this estimated coefficient? est The standard error of the price coefficient is (Enter your response rounded to two decimal places) Suppose we had another focus group sample, ran a regression on that sample, and obtained the same coefficient on price but with a standard error five times as large What can you say about the statistical significance of the price coefficient in this second sample? rt A The price coefficient would be statistically significantly different than zero at the 0.05 confidence level Sulag 50,00 t-Val Stan would be would not beTo determine whether the revenue made trom selling ice creams in a smal shop (in USD) and the temperature (in Celcius degrees) are related, a researcher decides to employ the simple linear regression analysis. Using a random set of days in which the temperature varies between 20 and 35, she comes up with the following regression line: Ice Cream Revenue- 200 90 Temperature Based on this analysis, what can she conclude? O A)At 20 Celcius degrees. the shop owner can xpect to sell 5000 USD O B)AI 30 Celoius degrees, the shop owner can expect to sel 2000 usD O C)As the temperature goes up by one degree Celoius, the revenue increases by approximately 00% OD)On average ce cream revenue is about 200 USD when the temperature is O degrees Celcus O E)As the temperature goes up by one degree Celcius. the reverue inereases by approximately 200 USD.
- Zeitler’s Department Stores sells its products online and through traditional brick-andmortarstores. The following parallel coordinates plot displays data from a sample of20 customers who purchased clothing from Zeitler’s either online or in-store. The datainclude variables for the customer’s age, annual income, and the distance from the customer’shome to the nearest Zeitler’s store. According to the parallel coordinates plot, howare online customers differentiated from in-store customers?Q7. Do quadretic regression to find the forcast value of quauter 9 and 10 Quarters (x) 1 2 3 4 5 6 7 8 9 10 Demand (y) 5.10 11.40 22.70 35.00 64.22 81.77 115.50 149.90The 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
- When running a ols regression, if one of my 3 control variables are insignificant via T-test should I keep them in the regression/how should I interpret them?Can you help me examine the relationship between both graphsSally Sells Sea Shells by the Sea Shore and collects all sales dataNow she is curious to find out what the elasticity of demand is for her shells Assume they are all the same type and quantity She scatter plots the data and finds there is a linear relationship that looks ripe for a regression estimation of the price response function for her shells The slope of her regression line is 61. Currently, her average daily price is 11.74 and she sells 95 quantity at that priceCalculate the point elasticity of demand for her sea shells
- Question 19 An economist wants to estimate the relationship between earnings (in thousands of dollars) and years of education. She estimates the model Earnings BO+B1 *Education + E. The following is a portion of her results. Coefficient Standard Error Intercept 15.77 Education 4.21 Which of the following is true? 3.8 1.4 p-value 0.003 0.032 O If education is increased by one year, we predict that earnings will increase by $4,210. O If earnings are increased by $1000, we predict that education will increase by 21 O If education is increased by one year, we predict that earnings will increase by $3200. O If earnings are increased by $1000, we predict that education will increase by .032 years,"In the regression model InY=b0+b1*InX+u, the coefficient b1 is interpreted as" O the intercept O A covariance O A regressor O An elasticity265 guizres/276906/take Grouping Information Using the lukey Method and .unf.educ Grouping ActivityT N Mean 9 145 444 A shop B. date 9 62.333 Means that do not share a letter are significantly different. Tukey Pairwise Comparisons: Age Grouping Information Using the Tukey Method and 95% Confidence Age N Mean Grouping mid 6 137.167 A old 6 98.500 A B. yng 6 76.000 Means that do not share a letter are significantly different O Marketers should focus on middle age rather than younger groups O Marketers should not pay more for access to middle age rather than older groups O All of the answers are correct. O Marketers should not pay more for access to older groups vs younger groups