3. a) Consider the following model for the demand function: Where Q Quantity demanded P price e e...
2. Consider the simple linear regression model: where e1, .. . , es, are i.i.d. N (0, o2), for i= 1,2,... , n. Suppose that we would like to estimate the mean response at x = x*, that is we want to estimate lyx=* = Bo + B1 x*. The least squares estimator for /uyx* is = bo bi x*, where bo, b1 are the least squares estimators for Bo, Bi. ayx= (a) Show that the least squares estimator for...
Consider the simple linear regression model y - e, where the errors €1, ,en are iid. random variables with Eki-0, var(G)-σ2, i-1, .. . ,n. Solve either one of the questions below. 1. Let Bi be the least squares estimator for B. Show that B is the best linear unbiased estimator for B1. (Note: you can read the proof in wikipedia, but you cannot use the matrix notation in this proof.) 2. Consider a new loss function Lx(A,%) 71 where...
Econometrics
13) Consider the classical linear regression model y = XB + E, EN(0,021) The data are collected in such a way that the X matrix is orthogonal, that is X'X = 1. We want to test the null hypothesis that Ho: B1 + B2 + ... + Bx = 0. For this particular hypothesis, the standard t-test for a single linear restriction r' B = q reduces to ki bi a) t= i=1 b) t = svk Ek=1b c)t...
7. Consider the following sample regression equation = 150 – 20x, where y is the demand for Product A (in thousands) and x is the price of the product A (in $). a) What is the value of the correlation coefficient when the R2 value for the above equation is 0.65? b) What kind of relationship is there between y and x? Describe the strength and direction. c) Estimate the demand for Product A when the price is $5? d)...
Consider the following model: log (YA) = Bo + B1S; + Balog(P) +€i where Y; denotes the mean hourly wage for individual i, S; denotes the number of years of education individual i has completed, and Pi denotes mother's education. Question 1 0/1 point (graded) Which of the following statements are true? Select all that apply. B1 is the elasticity of wage with respect to education. Each additional year of education leads to a (B1 * 100) % change in...
Consider the following demand and supply functions: where d is the quantity demanded, Q is the quantity supplied, P is the price, and all pa- rameters [ao, αι, βο'Al are positive constants unless otherwise stated. Denote θ as the partial derivative symbol, and Δ as the discretized units of change 1. (1 point) Derive the demand curve. What is the slope of the demand curve? A. 1 2. (1 point) What is the intercept of the demand curve (along the...
I will rate, please help!!!
Consider the following data concerning the demand (y) and price (x) of a consumer product. Demand, y Price, x 247 230 $2.06 $2.20 $2.47 $2.67 $2.88 $2.96 253 244 220 235 Type the data into Minitab as two COLUMNS (labeled Y (demand) and X (price)). Create a scatterplot to see the relationship between demand and price (a) From the plot, does it seem reasonable to use the simple linear regression model to relate y to...
Consider the following numerical model: C = 700 + 0.8YD I = 500-2000i+0.1Y G = 400 T = 500 - Find the equation for the IS curve (keep in mind that YD=Y-T). If you were to draw the IS curve, what would the intercept (where the IS curve crosses the Y vertical axis) be? (and find the intercept in relation to Y - ie in the form Y=a-bi where a is the intercept) - If G increases from 400 to...
1. Consider a variant of the two-period model of consumption-saving behavior. In this version of the model, the consumer has income y in the first period and no income in the second period. Her life-time budget constraint is c+ a - 1+r = y. (a) Draw this budget constraint in a diagram with con horizontal axis and d on vertical axis. What are the slope and vertical intercept of this budget constraint? Label the endowment point in the diagram. (3...
Consider the following simple regression model: where the e, are independent errors with E(ed-0 and var(et)-Ơ2X? a. In this case, would an ordinary least squares regression provide you with the best b. c. linear unbiased estimates? Why or why not? What is the transformed model that would give you constant error variance? Given the following data: y = (4,3,1,0,2) and x = (1,2,1,3,4) Find the generalized least squares estimates of β1 and β2 (Do this by hand! Not with excel)