Module 4 Assignment for Applied Statistics

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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…

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Topic: Regression    Problem 3:  A researcher is interested in determining whether there is a relationship between grades and hours studied for statistics.   Hours studied(X) Grade on final(Y) 1 20 2 30 4 40 7 60 6 70 7 78 8 83 9 98   1- You are given data for Xi (independent variable) and Yi (dependent variable).      2- Calculate the correlation coefficient, r:             r =           -1 ≤ r ≤ 1     3- Calculate the coefficient of determination: r2 = =                0 ≤ r2 ≤ 1 This is the proportion of the variation in the dependent variable (Yi) explained by the independent variable (Xi)                4- Calculate the regression coefficient b1 (the slope):              b1 = = Note that you have already calculated the numerator and the denominator for parts of r.  Other than a single division operation, no new calculations are required.   5- Calculate the regression coefficient b0 (the Y-intercept, or constant):…

Other Companies (Part 2) You directed your research department to do some research on the demand for Tesla sedans. They selected BMW i3 Sedans and Chevy Bolts as comparative offerings.  Using regression analysis, the research department comes up the following estimate for yearly demand.  Qx = -40,000 -1*Px +0.02*M +2*PB +2*PC Where:  Px = $70,000, M = $150,000, PB = $65,000, PC = $40,000 a. Is the own price elasticity of demand for Tesla sedans at the point defined above elastic or inelastic? If Mr. Musk decides to raise his prices, what will happen to his revenue. b. PB and PC represent the price for i3 sedans and Bolt sedans respectively. Are these items compliments or substitutes when compared to Teslas? Give evidence to support your answer. c. Is the demand for Tesla sedans elastic or inelastic to price changes of BMW i3 and Bolt at the price points given in the problem? Interpret the result you find and explain what it means.

The following data relate the sales figures of the bar in Mark Kaltenbach's small bed-and-breakfast inn in portland, to the number of guest registered that week:                            week            guests         bar  sales                                 1                 16              $330                                 2                  12              $270                                 3                  18              $380                                4                   14              $315 a) The simple linear regression equation that relates bar sales to number of guests(not to time) is (round your responses to one decimal place):                           Bar sales = [___]+[___]X guests

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A manufacturer is developing a facility plan to provide production capacity for its factory. The amount of capacity required in the future depends on the number of products demanded by its customers. The data below reflect past sales of its products: Year Annual Sales (number of products) Year Annual Sales (number of products) 1 490 5 461 2 487 6 475 3 492 7 472 4 478 8 458 Use simple linear regression to forecast annual demand for the products for each of the next three (3) years, by using the tabular method  to: derive the values for the intercept and slope derive the linear equation plot the linear regression line develop a forecast for the firm’s  annual sales for each of the next three years

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1. An analyst from your firm used a linear demand specification to estimate the demand for its product and sent you a hard copy of the results: SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations ANOVA Regression Residual Total Intercept Price of X Income 0.38 0.14 0.13 20.77 150 df 2 147 149 SS 58.87 -1.64 1.11 10398.87 63408.62 73807.49 Coefficients Standard Error 15.33 0.85 0.24 MS 5199.43 431.35 t Stat 3.84 -1.93 4.63 F 12.05 P-value 0.00 0.06 0.00 Significance F 0 Lower 95% 28.59 -3.31 0.63 Upper 95% b. Which regression coefficients are statistically significant at the 5 percent level? a. Based on these estimates, write an equation that summarizes the demand for the firm's product. 89.15 0.04 1.56 C. When price is $10, what is the income elasticity for this product for an income level of 35?

QUESTION 17 I am trying to figure out how to measure an athlete's productivity. So, I have run a linear regression of a NBA player's salary (dependent variable) on a player's statistics including average points, assists, rebounds per game, and turnovers per game (the independent variables). The final model is: Salary = 1,000,000 * Points per game + 50,000 * Assists per game + 20,000 * Rebounds per game - 30,000 * Turnovers per game %3! Last year, Lebron James averaged 25 points per game, 8 assists per game, 8 rebounds per game and 4 turnovers per game. What is Lebron's predicted salary?

5.2 42 The following regression shows the impact of the number of rooms (ROOM) on the monthly rent of an apartment (in thousand Rands) (RENT) from a sample of 42 randomly chosen apartments in Parow: Dependent Variable: RENT Variable C ROOM r-square: 0.7180 Parameter -0.7705 2.1331 SE of regression: 2.3397 Std. Error 0.8233 0.2114 sample size = 42 What will be values of the parameters, variance and standard errors of the parameters, estimated variance of error terms, coefficient of determination and correlation coefficient, if RENT is measured in Rands and there is no change to the unit of measurement of the ROOM variable?

Suppose the Sherwin-Williams Company is interested in developing a simple regression model with paint sales (Y) as the dependent variable and selling price (P) as the independent variable. Complete the following worksheet and then use it to determine the estimated regression line. Sales Region Selling Price ($/Gallon) Sales (x 1000 Gal) i 2 Zi Yi Zith 1 15 160 2,400 225 25,600 2 13.5 220 2,970 182.25 48,400 3 16.5 140 2,310 272.25 19,600 4 14.5 190 2,755 210.25 36,100 5 17 140 2,380 289 19,600 6 16 160 2,560 256 25,600 7 13 200 2,600 169 40,000 8 18 150 2,700 324 22,500 9 12 220 2,640 144 48,400 10 15.5 190 2,945 240.25 36,100 Total 151 1,770 2,312 Regression Parameters Estimations Slope (B) Intercept (a) In words, for a dollar increase in the selling price, the expected sales will What is the standard error of the estimate (&)? O 14.889 12.180 13.342 gallons in a given sales region. What is the estimate of the standard deviation of the estimated slope (86)? O 2.636 2.157 2.362 Can you…

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5. Confounding variables and multiple regressions Suppose you are interested in studying the effect of square footage on the price of houses. You propose the following regression of housing prices on square footage: price - Bo + P sqft + u where price the price of the house. sqft = the square footage of the house residual Failing to account for the number of bathrooms in a house, which may influence housing prices and may be positively correlated with square footage, could lead to estimate of the effect . This issue of confounding variables would likely bias the estimate of

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3. To explain what determine the price of air conditioners, B.T. Ratchford, obtained the following regression results based on a sample of 19 air conditioners: R²=0.84 y=-68.236 +0.023x, +19.729x3, +7.653x (0.005) (8.992) (3.082) se= Where y the price, in dollars x2= the BTU rating of air conditioner x3 the energy efficiency ratio x, the number of settings se standard errors a) Interpret the regression results. b) Do the results make economic sense? c) At 5% significance level, test the hypothesis that the BTU rating has no effect on the price of an air conditioner vs. that it has a positive effect. d) Would you accept the null hypothesis that the three explanatory variables explain a substantial variation in the prices of air conditioners? Show clearly all your calculations.

GSU is trying to predict how price of books predict the quantity of books sold over the semesters. Perform a liner regression analysis, and and find the best model to predict quantity of books to stock in the book store. Make recommendation at setting the prices and quantity at their optimum values for maximizing quantity of books sold. Be prepared to discuss your analysis. Quantity Price 180 475 590 400 430 450 250 550 275 575 720 375 660 375 490 450 700 400 210 500

The table to the right contains price-demand and total cost data for the production of projectors, where p is the wholesale price (in dollars) of a projector for an annual demand of x projectors and C is the total cost (in dollars) of producing x projectors. Answer the following questions (A) - (D). (A) Find a quadratic regression equation for the price-demand data, using x as the independent variable. X 270 360 520 780 The fixed costs are $. (Round to the nearest dollar as needed.) ITTI y = (Type an expression using x as the variable. Use integers or decimals for any numbers in the expression. Round to two decimal places as needed.) Use the linear regression equation found in the previous step to estimate the fixed costs and variable costs per projector. The variable costs are $ per projector. (Round to the nearest dollar as needed.) (C) Find the break even points. The break even points are (Type ordered pairs. Use a comma to separate answers as needed. Round to the nearest integer as…

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Consider the following estimated regression model relating annual salary to years of education and work experience. Estimated Salary=11,681.31+3418.97(Education)+1194.78(Experience) Suppose two employees at the company have been working there for five years. One has a bachelor's degree (8 years of education) and one has a master's degree (10 years of education). How much more money would we expect the employee with a master's degree to make?

What does the value for the coefficient mean in the regression analysis of both the company ? P-Values - how its related to customer satisfaction in the regression analysis of both the company ?

The Ipod Touch has been out for several years now and a lot of data has been collected. There is a functional relationship between the Price of an IPod Touch and Weekly Demand. Below is a table of data that have been collected Price P ($) Weekly Demand S (1,000s) 150 207 170 208 190 192 210 190 230 185 250 169 A.. Find the linear model that best fits this data using regression and enter the model below (for entry round the slope value to nearest 0.01 and constant parameter to nearest 1) T(p) = Now answer these two questions: B.. What does the model predict will be the weekly demand if the price of an ipod touch is $191 ? (nearest 100) C.. According to the model at what should the price be set in order to have a weekly demand of 194,800 ipod Touches? $ (nearest $1) Note: In the "real" world Apple sold about 20 million Ipod Touch's from Sept. 2007-Sept. 2009

4. The model below explains CEO salary (salary) expressed in thousands of pounds as a function of a firm' s sales in million pounds (sales), the return on a firm's equity (roe), and the industry in which the firm is operating. There are two industries in the sample, services and consumer goods. These industries are captured respectively by two dummy variables, service and goods. The regression based on a sample of 209 firms is as follows: = 4.5 + 0.27sales + 0.015roe - 0.08service (0.24) (0.03) (0.05) (0. 05) L1090 Introduction to Econometrics R-squared = 0.35 SSR(Residual Sum of Squares) = 42.9 a. Interpret the coefficient of service. b. In the regression model, the consumer goods as an industry is omitted from the model. Explain the implications of adding the binary variable goods to the regression model.

What is difference between regression model, and estimated regression equation?

Question 9 Regression analysis was applied between demand for a product (Y) and the price of the product (X), and the following estimated regression equation was obtained. Y = 120 - 15 X Based on the above estimated regression equation, if price is increased by 2 units, then demand is expected to: O Increase by 120 units Decease by 30 units O Increase by 2Q units Next « Previous Submi No new data to save. Last checked at 9:51pm

O Macmillan Learning A study is designed to examine the relationship between employees' job satisfaction and the amount of sleep they get. Think about creating a data set for this study. Assume that job satisfaction is measured by a scale of 1 (very dissatisfied) to 5 (very satisfied). Cases: Label Variable(s): Quantitative Variable(s): Categorical Variable(s): Explanatory Variable(s): Response Variable(s): Employee's name Answer Bank Job satisfaction Employees Amount of sleep

Hello,  I am trying to find the equations on my calculator for the price-demand and price supply equations. The data is in the attached image.  I think I am doing something wrong, but not sure what.  I found the quadratic regression model for the first set of data using my calculator, but I used the p=D(x) as list one, and x, as list two. I came up with  0.028x^2-23x +5743  is this right? or do I need the reverse the order?    For the price-supply data I but the p=S(x) as list 1 and x as list 2 and I got the linear regression function: 2 5.1x+342   Can you please let me know if I am on the right track?