Question 2. Which of the following models can be estimated (following a suitable transformation if necessary) using ordinary least squares (OLS), where x, y, z are variables and a, B, y are parameters to be estimated? a) y, = eªx,"ei b) y, = a + Bx, + ɛ, c) In(y,) = a + ß In(x,)+E, d) y, = a + Bx,z, + ɛ,
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- A student prepared the following spreadsheet model to calculate the final price of clothing items which are sold at a discount. To be complete, the student included a calculation of sales tax in the final price, given the original price (180), discount (0.2), and sales tax rate (0.09) shown below. A B 1 2 Original Price 180 3 Discount(%) 0.2 4 Discount ($) = B2 × B3 5 Net Price = B2 − B4 6 Sales Tax(%) 0.09 7 Sales Tax($) = ROUND(B5 × B6,2) 8 Final Price = ROUND(B5 + B7,2) Determine what values the spreadsheet should display. (Round your answer to 2 decimal places.)Determine the mode choice (personal vehicle or bus system) for the following regression model: Utility Function: Umode – (8.333 x 10-4)*(Access time in sec) – (6.667 x 10-4)*(Wait Time in sec) – (5.00 x 10-4)*(Riding time in sec) – (1.40)*(Cost, $) PARAMETER PERSONAL VEHICLE CITY BUS SYSTEM MODE CONSTANT -0.01 -0.07 ACCESS TIME (SECS) 300 600 WAITING TIME (SECS) 0 900 RIDING TIME (SECS) 1,500 6,000 COST (DOLLARS) $1.50 $1.004. The estimation of the model with quarterly car sales in the U.S. from 1975 to 1990 gives: Source | df MS Number of obs = 64 F( 2, Prob > F 61) = 12.21 Model .32720224 2 .16360112 0.0000 Residual | .817286587 61 .013398141 R-squared Adj R-squared = 0.2625 Root MSE 0.2859 Total | 1.14448883 63 .018166489 .11575 lqne | cCoef. t P>|t| std. Err. [95% Conf. Interval] 1price lincome -.4604611 3.37186 6.89398 -.8280926 .1838504 -4.50 0.000 -1.195724 2.399991 . 4860261 4.94 0.000 1.428121 _cons 5.92543 .4843662 12.23 0.000 4.95688 Based on the parameter estimates, what is the predicted effect of a 10% increase in price on the number of cars sold? What would be the effect of that price increase on the value of car sales?
- Styles 6. The following two regression models are Probit and Logit respectively: Pr(Y=1|X)=(Bo+Bi xXr+Bzx X2) Pr(Y=1|X)=F(Bu + B₁ × Xs + B₂ × X2) (a) what functions do and F represent? (b) How do Probit, and Logit ensure that the predicted probabilities are always between 0 and 1? (c) Sketch a graph of the Y= $(Z) function. (Z on the horizontal axis, Y on the vertical axis) (d) What estimation method is used to estimate the coefficients in a Probit/Logit model? (e) What are the two measures of fit for models with binary dependent variables? Focus 88 B E1) Production function for agricultural sector of a country is specified as the following, log Y=B1 + B2 log K+ ß3 log L+u. where Y represents wheat output, K capital stock and L employment (labor). The model is estimated using annual data over 1980-2020 (n=41) periods. The results are reported below. p-values are given in squared parentheses. loĝ Y = 4.17 +0.67 log K+ 0.35 log L p-value [0.015] [0.18] R² = 0.81 1.a) Test if each slope coefficient is significant individually (one by one) using the p-values in parentheses and interpret the results. (Critically/quantitatively evaluate the following statement (true, false or uncertain): • In a linear model, the Generalized Instrumental Variable (GIV) estimator BGIV is iden- tical to the Ordinary Least Squares (OLS) estimator BoLS.
- A linear regression model for the revenue data for a company is R=27.1t+203 where R is total annual revenue and t is time since 1/31/02 in years. 12 months 12 months 12 months Billions of Dollars Revenue Gross Profit 12 months 12 months ending 1/31/02ending 1/31/03ending 1/31/04 ending 1/31/05 ending 1/31/06 500- 201 49 236 54 255 60 500- 277 65 (A) Draw a scatter plot of the data and a graph of the model on the same axes. OA. B. O.C. KICB Q 2 316 72 500- oo D. 500- Q GThe average remaining lifetimes for women of various ages in a certain country are given in the following table. (A graphing calculator is recommended.) Average Remaining Lifetimes for Women Age (x) Years (y) 80.6 15 65.5 35 46.9 65 19.1 75 12.8 (a) Find the equation of the least-squares line for the data. (Round all numerical values to two decimal places.) (b) Use the equation from part (a) to estimate the remaining lifetime of a woman of age 19. (Round your answer to the nearest year.) yr (c) Is the procedure in part (b) an example of interpolation or extrapolation? O interpolation O extrapolationThe following two equations were estimated using the data in MEAPSINGLE. The key explanatory variable is lexppp, the log of expenditures per student at the school level. math4 = 24.49 + 9.01 lexpp – 422 free – .752 Imedinc – .274 pctsgle (.071) (59.24) (4.04) n = 229, R² = .472, R² (5.358) (.161) 462. 149.38 + 1.93 lexppp – .060 free – 10.78 Imedinc – .397 pctsgle + .667 read4 (3.76) math4 (41.70) (2.82) (.054) (.111) (.042) n = 229, R = .749, R = .743. (i) If you are a policy maker trying to estimate the causal effect of per-student spending on math test performance, explain why the first equation is more relevant than the second. What is the estimated effect of a 10% increase in expenditures per student? (ii) Does adding read4 to the regression have strange effects on coefficients and statistical signifi- cance other than Brexppp? (iii) How would you explain to someone with only basic knowledge of regression why, in this case, you prefer the equation with the smaller adjusted…
- Interpret the slope (m) and R2 values given in the equation of linear regression for both costs and benefits.regression result for your product is shown in the table below: Variable Parameter Estimates Standard error Constant -164.0 20.24 Price of good X (P,) Price of good Y (P,) -3.50 1.55 2.50 0.28 Per capita Income (/) 0.45 0.52 R-squared Adjusted R-squared 0.8672 0.8132 F-statistic 15.6893 a) Suppose the average price of 3 units of good X is GH¢12, price of 2 units of goodY is GH¢60, the per capita income of Ghana is GH¢420. i. Write down the estimated demand equation for your firm's product and interpret the parameter estimates. Determine the quantity of good X sold. Estimate the own price elasticity of demand and state the type of demand curve 11. 111. your firm has? What would be the effect of a price increase on the firm's total revenue? iv. Assess the probable impact on your firm if the firm producing geod Y decreases their price by 10%. Explain the adjusted R-squared Is the good X a normal or inferior good? What is the relationship between good X and good Y? V. vi. vii. viii..Consider the following estimated regression for 220 home sales from a community in 2019 (estimated standard errors in parentheses) Price = 119.2 + 0.485BDR + 23.4Bath + 0.156Hsize + 0.002Lsize + 0.09Age (0.011) (2.61) (8.94) (0.00048) (0.311) R2 = 0.72 where Price denote the selling house price (measured in $1000s), BDR denote the number of bedrooms, Bath denote the number of bathrooms, Hsize denote the size of the house (in square feet), Lsize denote the lot size (in square feet), and Age denote the age of the house (in years).