a) In such a scenario, we cannot fit a linear regression line to our model. The effect of a marginal change in X on Y is not constant. It depends on the value of X. Hence the slope coefficients do not have their usual interpretation.
Now, for a continuous independent variable X, the marginal effect (given by its coefficient ) is the first derivative of the response function Y with respect to X. However, if X is a categorical variable (say a binary variable that can take two values 0 and 1), then the marginal effect is the difference in the adjusted probabilities of these two groups.
b) We can use the double log transformation to consistently estimate this production function.
where we add , a random disturbance term to the model .
This equation can be estimated via regression analysis given data on Y, K and L.
c) Detecting non-linearity
i) Use scatter plots in stata to find a non linear relation between the dependent and independent variables. Command in stata- scatter . Further use lfit command to show a linear fit.
ii) Plot residuals versus each of the independent variable. Finding a non-random pattern is indicative of non-linearity.
Question 4 (15p): Nonlinear estimation a. In a nonlinear BoBiXi+B2X?+ b. Consider the model Y =...
Question 3 [4 points] Suppose the model is: Y B1+B2Xu. What is the nonlinear regression algorithm to estimate the model (i.e., list the steps to estimate the coefficients)?
Need help with stats true or false questions Decide (with short explanations) whether the following statements are true or false a) We consider the model y-Ao +A(z) +E. Let (-0.01, 1.5) be a 95% confidence interval for A In this case, a t-test with significance level 1% rejects the null hypothesis Ho : A-0 against a two sided alternative. b) Complicated models with a lot of parameters are better for prediction then simple models with just a few parameters c)...
gold ($/oz) Y copper (cents/lb) X1 silver ($/oz) X2 Aluminum (cents/lb) X3 161.1 64.2 4.4 39.8 308 93.3 11.1 61 613 101.3 20.6 71.6 460 84.2 10.5 76 376 72.8 8 76 424 76.5 11.4 77.8 361 66.8 8.1 81 318 67 6.1 81 368 66.1 5.5 81 448 82.5 7 72.3 438 120.5 6.5 110.1 382.6 130.9 5.5 87.8 Statistics 11 Homework 9 Due Wednesday, Nov. 20 Metals.jmp lists the yearly average price of gold, copper, silver, and aluminum....
7 Consider the following regression output involving the variables y and, rı, r2. (note log is the natural logarithm as usual) 4.12 0.88 r Model A: Model B: log(y)0.34 0.14 + 0.001 2 Model C: logly)2011.4 log()0.02 r2 0.06 Model D: Model E: y = 5.4 + 0.82i --3.4 55.1 log(0.020 2 + 1.2r2 0.2 (1x2) Ceteris Paribus: (a) In Model A: If x1 increases 6 to 8 by 2 units, then the predicted change in y is Δy =...
Question 1 (a) (4 points) What are they key advantages of the Logit model over the Linear Probability Model? (b) (15 points) In class we saw that efficient estimates of the coefficients from a linear regression model can be obtained under the presence of heteroskedasticity using Generalized Least Squares (GLS). How does GLS work? That is, describe the mechanism through which GLS addresses non-constant error variances to achieve efficient estimation. (c) (5 points) Let Zi be the log-odds ratio in...
Hi, can you please explain the steps you would do for this problem using a graphing calculator Consider the following Regression Model: The top law firms in the world in terms of profit per equity partner and the gross revenue ($ millions) for the most recent fiscal year were analyzed. Given this information, answer the question using the provided output. Coefficients Coef SE t p Intercept 65.8 11.7 5.61 0.00 Gross_revenue .1682 .0127 13.21 0.00 Analysis of Variance Source df ...
Question #1 Consider the following model that predicts X20 (Likely to recommend) Model Summaryb ModelR RSquare Adjusted R Square Std. Error of the Estimate 7270.529 0.511 0.7570 ANOVA' Sum of Squares df Mean SquareF Si | 30.753 | .000ь 123.346 10.013 233.359 17.621 0.573 sion Residual Total 192 199 Coefficients Unstandardized Coefficients StandardizedtSig Coefficients Model Std. Error 0.671 0.049 0.060 0.062 0.050 0.063 Beta (Constant) X6 - Product Quality X8 Technical Su X10- Advertisin X11 Product Line X12 Salesforce Ima...
For this exercise we will run a regression using Swiss demographic data from around 1888. The sample is a cross-section of French speaking counties in Switzerland This data come with the R package datasets. The first step is to load the package into your current environment by typing the command libraryldatasets) in to the R console. This loads a number of datasets including one called swiss. Type help/swiss) in the console for additional details. The basic variable definitions are as...
3) Consider the following linear regression: y =a + Bx + Show that minimizing the sum of squared residuals ( - ) to obtain OLS estimators of the slope and the intercept results in the following algebraic properties a) b) Ex = 0 = 0 4) You run the following regression: TestScore = a + (Female) + where TestScore is measured on a scale from 400 to 1000, and female is an indicator for the gender of the student. You...
We consider a multiple linear regression model with LIFE (y) as the response variable, and MALE (x1), BIRTH (x2), DIVO (x3), BEDS (x4), EDUC (x5), and INCO (x6), as predictors. "STATE" "MALE" "BIRTH" "DIVO" "BEDS" "EDUC" "INCO" "LIFE" AK 119.1 24.8 5.6 603.3 14.1 4638 69.31 AL 93.3 19.4 4.4 840.9 7.8 2892 69.05 AR 94.1 18.5 4.8 569.6 6.7 2791 70.66 AZ 96.8 21.2 7.2 536.0 12.6 3614 70.55 CA 96.8 18.2 5.7 649.5 13.4 4423 71.71 CO 97.5...