r= 8/15. Find (i) the regression coefficient of X on Y (ii) the regression coefficient of Y on X (iii) the most likely value of Y when X = Rs 100.
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- Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?Consider a simple linear regression model Y=α+βX+ε. We have collected 15 samples, from which we calculated the summary statistics ∑xi=66, ∑x2i=6568, ∑yi=459, ∑y2i=27933, ∑xiyi=11311. Suppose one of the data is supposed to be (x1=10, y1=30), but is incorrectly recorded as (x1=7, y1=34). All other observations are correctly recorded. What is the OLS estimators αˆ= ? and βˆ= ? based on the correct data.A. Identify the regression analyses necessary for testing this initial model. B. What are the direct and indirect effects of z2 on z5?
- Suppose we want to predict job performance of mechanics based on mechanical aptitude test scores and test scores from personality test that measures conscientiousness. (a) Determine the regression equation. (b) Determine the SSE. Y X1 X2 1 40 25 2 45 20 1 38 30 3 50 30 2 48 28 3 55 30 3 53 34 4 55 36 4 58 32 3 40 34 5 55 38 3 48 28 3 45 30 2 55 36 4 60 34 5 60 38 5 60 42 5 65 38 4 50 34 3 58 38 Where Y is the Performance of the mechanics, X1 is the mechanical aptitude test and X2 is the personality test score that measure conscientiousness.I have some doubts regarding linear regression. if any 2 variables in X1, X2 AND Y have a positive correlation, then in the linear regression Y = b0 + b1X1 +b2X2 +e, will the sign of b1 and b2 both be positive? will the residuals that we get from linear regression will always be uncorrelated given X?justify the reasons for the in1.Econometrics deals with the measurement of economic relationships which are stochastic or random. The simplest form of economic relationships between two variables X and Y can be represented by: ; where are regression parameters and the stochastic disturbance term Justify the reasons for the insertion of U-term in the modelsertion of of u (error term) in the model Y=a+bX+u?
- There is a linear regression: Yi = B0+ B1(Xi^2)+ ei present, where Xi is squared. ei ∼ N(0,σ2). How would I derive LSE for B0 and B1 and their variance?Just parts d,e anf f of question 1 d) We conduct a simple regression of size on hhinc, now using robust standard errors. The regression output is reported in Table 2. Why are the estimated coefficients in Table 2 equal to the estimated coefficients in Table 1? Do the conclusions on the statistical significance at 5% of the coefficient of hhinc change between Tables 1 and 2? e) Now, using both the critical value and the p-value, test whether the coefficient of hhinc is statistically significant at 1%, by using the results in Table 1. Repeat the test by using the results in Table 2. Compare the results based on Table 1 with the results based on Table 2. Consider the results in Table 2. Compute the 99% confidence interval for hhinc. f) Consider the results in Table 2.How would you decide whether 0 is contained in the 99% confidence interval for the coefficient of hhinc, without actually computing the confidence interval?If there is a positive correlation between X and Y then in the regression equation, Y = bX + a, ____.
- Suppose that the sales of a company (Y) is regressed on advertising expenditure (x) and labor cost (z), and the estimated regression equation is Y = 5 + 0.5x + 0.7z + u (where u is the error term). Here, sales, advertising expenditure and labor cost are measured in million Tk. Standard error for the coefficient of x is 0.04, standard error for the coefficient of z is 0.01, and the sample size is 20. Can we conclude that advertising expenditure is a statistically significant variable?For the regression model Yi = b0 + eI, derive the least squares estimator.The first step of the Durbin-Watson test for the presence of autocorrelation is to estimate the model and determine Select one: a. the residuals lagged one period. b. the current period residuals and the residuals lagged one period. c. the current period residuals. d. the current period residuals, the residuals lagged one period, and the residuals lagged two periods.
