Let there be a simple regression yt = (alpha) + (beta)x + (ε), where ε~?(0, σ^2) Let ε(hat) be an OLS estimator of ε. Prove Sum(ε(hat)) = 0
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Can you solve the following: and provide workings?:
1) Let there be a simple regression yt = (alpha) + (beta)x + (ε), where ε~?(0, σ^2)
Let ε(hat) be an OLS estimator of ε. Prove Sum(ε(hat)) = 0
2)Let the share price of a listed company, S, have the following distribution:
S~N(100,225)
a)Suppose that, when the price of this share falls below the 10th percentile of its
distribution, it is a signal for buying. What is the maximum price at which you would
buy this share?
b) Suppose that, when the price of this share rises beyond the 90th percentile of its
distribution, it is a signal for selling. What is the minimum price at which you would
sell this share?
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- (Yi, X1i, X2i) satisfy the assumptions. You are interested in β1, the causal effect of X1 on Y . Suppose that X1 and X2 are uncorrelated. You estimate β1 by regressing Y onto X1 (so that X2 is not included in the regression). Does this estimator suffer from omitted variable bias? Explain.BUS – 173 (Applied Statistics) # Determining if the following statement are True and False. If False, write the correct statement. Also Solve the MCQ 01. In the Simple linear regression model, components of the random error term are assumed to be independent (a) True (b) False 02. The possible for the perfect negative correlation is +1 (a) True (b) False 03. The possible range of coefficient of determination (r^2) is -1 to 1 a) True (b) False 04. A scatter diagram is a - (a) two-dimensional graph of a straight line (b) two-dimensional graph of a curved line (c) two-dimensional graph of a data points (d) one-dimensional graph of randomly scattered dataTom has been gathering data concerning the cost of a spa treatment, y', during the before Valentine's Day. The only independent variable that he has considered is the number of minutes, "x," in the treatment. Suppose Tom collects data on the relationship between the number of minutes in a treatment and the resulting cost of we the treatment. Tom finds that the correlation between cost and number of minutes is strong and positive. Therefore, he has performed a linear regression analysis on his data. His results are that the constant "a" is 35, and the coefficient "b1" for the independent variable is 1.3. Which of the following is the correct linear regression equation that would allow Tom to predict the cost of a spa treatment given the number of minutes? Oy = 78x + 35 Oy' = 1.3x + 35 %3D Oy = 78x - 1.3 %3D OY = -1.3x - 35
- After studying the milk yields of a randomly selected sample of 900 cows, researchers felt that the presence of white spots (WS;) on a cow's body led to a different level of milk production (MP;). The researchers estimate the OLS regression: where WS, is a binary variable of the form: WS₁ = MP = 5.36 +0.26 x WS₁, (2.23) (0.06) 1, if the th cow has white spots 0, if the th cow doesn't have white spots The 95% confidence interval for the coefficient ₁ is (₁). (Round your answers to four decimal places.) Based on this interval, we will the hypothesis P₁ = 0 at the 5% significance level. Which of the following statements describes the way in which the coefficient of the indicator variable could be interpreted in this case? O A. The coefficient is the sum of the conditional expectation of the presence of white spots on a cow with respect to the average milk production. OB. The coefficient is the rate of change in the milk production due to a unit change in the number of cows with white…Given 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.…
- 8- 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 increaseThe article "The Undrained Strength of Some Thawed Permafrost Soils"+ contained the accompanying data on the following. y = shear strength of sandy soil (kPa) x₁ = depth (m) x₂ = water content (%) The predicted values and residuals were computed using the estimated regression equation y = -156.50 - 16.52x₁ + 13.83x₂ + 0.100x3 -0.258x4 +0.496x5 ₁², x₁ = x₂², and x5 = X1X2• where x3 = y X1 14.7 8.8 31.4 48.0 36.5 26.9 25.6 36.9 25.8 x2 10.0 6.2 39.2 16.0 6.8 39.3 20.7 16.8 7.0 38.4 7.4 33.8 38.8 8.3 33.9 16.9 6.4 27.0 8.1 33.2 24.9 10.0 12.8 28.0 16.0 4.4 26.2 37.9 7.3 2.8 34.7 1.9 36.5 Predicted y 22.86 46.10 27.38 11.23 13.47 16.80 23.55 25.24 15.75 24.47 15.19 29.93 15.51 8.00 Residual -8.16 1.90 -1.78 -1.23 2.53 0.00 -2.85 13.56 1.15 2.53 0.81 -5.03 -8.21 4.80 (a) Use the given information to calculate SSResid, SSTO, and SSRegr. (Round your answers to four decimal places.) SSTO = SSResid = SSRegr = (b) Calculate R² for this regression model. (Round your answer to three decimal…Suppose we have fit a multiple linear regression with 8 explanatory variables and an intercept with 85 observations. We want to test the joint significance of the first 5 explanatory variables using an F test. Please fill in the blanks for the numerator and denominator degrees of freedom of the F statistic of the test: "The F statistic is F(
- With t test statistics and its p-value, given in the regression output, we test: O a. a joint hypothesis about significance of all parameters except constant O b. a single hypothesis about insignificance of R^2 O C. a single hypothesis about significance of parameter O d. a joint hypothesis about insignificance of all regression parametersThis table reports the regression coefficients when the returns of the size-institutionalownership portfolio (columns 1 and 2) returns are regressed on three variables: a constant(column 3), the stock market returns (column 4), and the change of the value weighted discountof the closed end fund industry (column 6). Columns 5 and 7 report the corresponding t-statistics of the coefficient estimates. Note that a t-statistic with an absolute value above 1.96means the coefficient estimate is significantly different from 0 at the 1% level. Column 8reports the R square of the regressions. Column 9 reports the mean institutional ownership ofeach portfolio. The last column reports the F-statistics for a multivariate test of the null hypothesis that the coefficient on ΔVWD in the Low (L) ownership portfolio is equal to theHigh (H) ownership portfolio. Two-tailed p-values are in parentheses. 1. What is the main finding of this Table? 2. What is the explanation for…An investigation into the relationship between an adolescent mother's age x in years and the birth weight y of her baby in grams yielded the regression equation y= - 1163.45 + 245.15x as well as r = .88369, r2= .78091, SSE = 337212.45, and s= 205.30844 1) What is the predicted birth weight for a baby brn to a 17 year old woman? 2) What is the propotion of the variability in the weights of babies born to adolescent mothers that is accounted for by the mother's age? 3) For every additional year in the mother's age that mean birth weight of the baby? (a) increases by about 245g (b) decreases by about 245g (c) increases by about 1163g (d) increases by about 1163g (e) changes by an amount that cannot be determined from the information given.
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