When using the method of least squares to estimate the parameters in multiple linear regression, we assume that the model errors ar normally and independently distributed with mean zero and constant variance. True False
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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?In a multiple linear regression model with 2 predictor variables and 10 observations, what is the standard error of the estimate if the residual sum of squares is 45?In a simple linear regression, show that the OLS regression line always passes through the mean (average) of both x and y.
- What are the Assumptions of Extended Least Squares in the Multiple Regression Model?In a multiple linear regression model with 3 predictor variables, what is the t-statistic for the hypothesis test of the null hypothesis that the coefficient of the second predictor variable is equal to 0, if the estimated coefficient is 0.5, the standard error of the estimate is 0.1, and the degrees of freedom is 15?Above, a table was created to calculate the coefficients of the linear regression y=ax+b model for a data set using the least squares method. What is the coefficient a in this model?
- The least-squares regression line relating two statistical variables is given as = 24 + 5x. Compute the residual if the actual (observed) value for y is 38 when x is 2. 4 38 2The most common methods used to ‘fit’ a straight line to a dataset with a continuous outcome and predictor variables is called the least squares regression method. True FalseFor a least squares regression line, the sum of the residuals is __________. always negative sometimes positive and sometimes negative always zero always positive
- 1) Indicate whether the following statements are true or false. Explain why and show your work.a) In a simple regression Yi = B1 + B2 Xi + ui where var(ui) = o^2.X^2, weighting the model by X would solve the problem of non-common (heteroskedastic) variance of the error term.When a regression coefficient in a multiple linear regression model is zero, the slope of the corresponding independent variable is zero. True FalseDefine with proof Least Squares Regression Variance of α^ & β^