Can I include the dummy variables in regression equation like Y=a+bX+u where the X is the vector of x variables that contain dummy variables with 5 categories? how should I write my general regression equation with this?
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- What is a linear regression model? What is measured by the coefficients ofa linear regression model? What is the ordinary least squares estimator?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…(2)What would the consequence be for a regression model if theerrors were not homoscedastic?
- 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…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. 2009QUESTION 2 Continue to use the example from Question 1. Suppose each product is randomly assigned to a process by a computer program, but some products get reassigned on the factory floor (for practical reasons). Let Z¡ denote the original assignment and X¡ the actual process used to produce i. In a regression of Y¡ on X¡ and Wj, OLS is: d. Potentially biased because W; should not be included b. Potentially biased, but an IV regression using Z¡ as an instrument can be used to obtain a consistent estimator C. Unbiased because the products were randomly assigned in the beginning d. Unbiased as long as Zj is also included as a control variable
- Using the data below, what is the slope coefficient from a regression of Quantity on Price? It is probably easiest to use either Gretl or Jamovi as in the powerpoint example. (round your answer to the nearest 0.1, and it can be either positive or negative.) Quantity 17 24 23 39 55 54 60 76 71 80 Price 93 77 62 64 47 35 38 12 29 25. 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 ofIn IS-MP model what variable is on horizontal axis? If IS-MP have different variable on horizontal axis how can we put these two curves into one diagram?
- The table below shows the profit, P(x), in dollars, from selling x items. 1 2 3 6 9 14 P(x) 66.1 82.4 88.9 49.6 -77.9 -486.4 Using your calculator to do a quadratic regression, express the profit as a function of the number of items sold. P(x) = Round all numbers to 1 decimal place. Using your quadratic regression, estimate the profit from selling 5 items? Select an answer v Round to 2 decimal places. Using your quadratic regression, estimate the number of items that need to be sold to make a profit of $-25.6 ? Select an answerSuppose that you had data on the amount of pollution in London every year. Write down the regression equation that you would need to estimate to measure the effect of ULEZ on pollution. Describe carefully what the dependent variable, the independent variable, the unit of observation (time or location), and the main coefficient of interest are. What control variables do you think should be included in this regression?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…