Consider multiple regression in matrix setting. LSE estimators beta hat=(X'X)^-1X'Y,with mean od beta and covariance of sigma^2(X'X)^-1. Why the residual vector is uncorrelated with the LSE estimators?
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Consider multiple regression in matrix setting. LSE estimators beta hat=(X'X)^-1X'Y,with mean od beta and
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- There is a relation between the following variables as y = 1 / (a * x ^ b) (x ^ b means x over b) a) Calculate the correlation coefficient and interpret the degree of the relationship? b) Estimate the y-value for x = 4.3 and the x-value for y = 0.90 by obtaining the regression equationA particular article presented data on y = tar content (grains/100 ft³) of a gas stream as a function of x₁ = rotor speed (rev/min) and x₂ = gas inlet temperature (°F). The following regression model using X₁, X2, X3 = ×₂² and ×4 = X₁X₂ was suggested. (mean y value) = 86.5 – 0.121x₁ +5.07x2 - 0.0706x3 + 0.001x4 (a) According to this model, what is the mean y value (in grains/100 ft³) if x₁ = 3,400 and x₂ = 55. grains/100 ft³ (b) For this particular model, does it make sense to interpret the value of ₂ as the average change in tar content associated with a 1-degree increase in gas inlet temperature when rotor speed is held constant? Explain. Yes, since there are no other terms involving X2. O Yes, since there are other terms involving X₂. ● No, since there are other terms involving X2. O No, since there are no other terms involving X2.Select True or False for each statement, depending on whether the corresponding statement is true or false. 1. Multicollinearity is a situation in which two or more independent variables are highly correlated with each other. 2. In a multiple regression problem, the regression equation is y^=60.6−5.2x1+0.75x2. The estimated value for y when x1=3 and x2=4 is 48. 3. In a multiple regression problem involving 24 observations and three independent variables, the estimated regression equation is y^=72+3.2x1+1.5x2−x3. For this model, SST=800 and SSE=245. The value of the FF statistic for testing the significance of this model is 15.102. 4. For each x term in the multiple regression equation, the corresponding β is referred to as a partial regression coefficient.
- There is a relationship in the form of Y = 1 / (a * x ^ b) (x ^ b: means x over b).a) Calculating the correlation coefficient and interpreting the degree of relationship?b) Estimating the y value for x = 4.3 and the x value for y = 0.90 by obtaining the regression equationGiven are five observations collected in a regression study on two variables. xi 2 6 9 13 20 yi 7 18 9 26 23 Compute b0 and b1 (to 1 decimal).b1 b0 Complete the estimated regression equation (to 1 decimal).^y = + x Use the estimated regression equation to predict the value of y when x = 6 (to 1 decimal).^y =A trucking company considered a multiple regression model for relating the dependent variable y = total daily travel time for one of its drivers (hours) to the predictors x₁ = distance traveled (miles) and x₂ = the number of deliveries made. Suppose that the model equation is Y = -0.800+ 0.060x₁ +0.900x₂ + e (a) What is the mean value of travel time when distance traveled is 50 miles and four deliveries are made? hr (b) How would you interpret ₁ = 0.060, the coefficient of the predictor x₁? O When the number of deliveries is constant, the average change in travel time associated with a ten-mile (i.e. one unit) increase in distance traveled is 0.060 hours. O The total daily travel time increases by 0.060 hours when the distance traveled increases by 1. O When the number of deliveries is held fixed, the average change in travel time associated with a one-mile (i.e. one unit) increase in distance traveled is 0.060 hours. O The average change in travel time associated with a one-mile (i.e.…
- Some non-linear regressions can also be estimated using a linear regression model (using 'linearization'). Assume that the data below show the selling prices y (in dollars) of a certain equipment against its age x (in years). We'd like to fit a non-linear regression in the form y = cd* to estimate parameters c and d from the data by linearizing the model through In y In c+ (In d)x = b, + b, x. y y 6381 3 5394 5673 4980 2 5740 4896 (Click the button to copy or download the data.) Using Excel ot other software, the non-linear regression model y = cd can be estimated as: y = D*. (Round c and d to four decimal places, inlcuding any zeros.)In a study, the simple linear regression equation was found as y = - 2.65 + 3.23 * x. Accordingly, if the value of x is 1.55, what will be the value of "y"? Biraraştımada basit doğrusal regresyon denklemi y-265+3,23xolarak bulunmuştur. Buna yöre xin değeri 1,55 olursa y'nin değeri ne olur?- 25 - O A) -2,36 O B) 2,36 O C) 6,32 O D) -7,66 O E) 7,668- According to the summary result of linear regression model between A and B obtained from R given below, we can fit a regression line. Assume that A has any value. If we decrease the value of A by 3, how would Y be affected? Call: Im (formula = B - A) Residuals: Min 10 Median 30 Маx -16.340 -10.793 -9.653 -8.502 58.325 Coefficients: Estimate Std. Error t value Pr (>[t]) (Intercept) 19.6315 20.6457 0.951 0.373 A 9.9609 0.3717 26.800 2.58e-08 *** --- Signif. codes: O *** 0.001 1** 0.01 1** 0.05 '.' 0.1 '' 1 Residual standard error: 26.46 on 7 degrees of freedom Multiple R-squared: 0.9903, Adjusted R-squared: 0.989 F-statistic: 718.2 on 1 and 7 DF, p-value: 2.58le-08 a) 49.5142 decrease b) 29.8827 increase c) 58.8945 decrease 29.8827 decrease 58.8945 increase
- We are interested in estimating the following model log(wage) = Bo + Bieduc + Bzexper + u where • wage=hourly wage, in US dollars; • educ=number of years of education; • exper=number of years of work experience. The variable ctuit is the change in college tuition facing students from age 17 to age 18 and is used as an IV for educ. We run the first stage regression for educ and get the following output: Source s df MS Number of obs 1,230 F (2, 1227) 550.19 Model 3220.84426 2 1610.42213 Prob > F 0.0000 Residual 3591.43541 1,227 2.92700523 0.4728 R-squared Adj R-squared 0.4719 Total 6812.27967 1,229 5.54294522 Root MSE 1.7108 educ Coef. Std. Err. t P>|t| [95% Conf. Interval] ctuit -.1859575 .0608175 -3.06 0.002 -.3052752 -.0666398 exper -.521161 .0157156 -33.16 0.000 -.5519933 -.4903286 _cons 18.63905 .1757961 106.03 0.000 18.29415 18.98394 Is the assumption of instrument relevance satisfied? Why yes, or why not?For the linear regression model Y = bo + b1(X): The p-value for the intercept is large: about 0.98 The p-value for the slope is very small: less than 2 times 10^(-16) What can we conclude? Since the p-value for the intercept is large, we can conclude that there is not a strong correlation between X and Y. Since the p-value for the intercept is large, we can conclude that there is a very strong correlation between X and Y. Since the p-value for the slope is very small, we can conclude that there is a very weak correlation between X and Y. Since the p-value for the slope is very small, we can conclude that there is a very strong correlation between X and Y. We are not able to assess the strength of the correlation between X and Y with the output provided.Consider the following population model for household consumption: cons = a + b1 * inc+ b2 * educ+ b3 * hhsize + u where cons is consumption, inc is income, educ is the education level of household head, hhsize is the size of a household. Suppose a researcher estimates the model and gets the predicted value, cons_hat, and then runs a regression of cons_hat on educ, inc, and hhsize. Which of the following choice is correct and please explain why. A) be certain that R^2 = 1 B) be certain that R^2 = 0 C) be certain that R^2 is less than 1 but greater than 0. D) not be certain
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