The researcher runs an OLS regression with five regressors and a constant on a sample of 453 observations. The value of R² for this regression is 0.4871. Subsequently she imposes two restrictions on the coefficients and runs a corresponding restricted regression. The value of R² is now 0.4703. Assuming that errors are homoskedastic, compute the F statistic for the test of joint validity of the two restrictions. Is the null hypothesis rejected? Based on your conclusion, are the two restrictions jointly valid?

In the multiple regression model with a quarterback's salary the response variable Y and the X variables pass completion percentage (PCT), number of touchdowns (TD), and age; the test of joint significance rejected HO: beta1 = beta2 = beta3 = 0. What does that mean? O Most of these X variables are significant in explaining salary. O At least one of these X variables is significant in explaining salary. O Each of these X variables is significant in explaining salary. O The model with all three X variables is significantly better than using sample mean salary alone to estimate expected salary

Suppose that you are interested in testing a joint null hypothesis consisting of three restrictions, say B, = B2 = B3 = 0 in multiple regression. Assume that you have three individual t-statistics for B; = 0, where j = 1,2,3. Consider the following testing procedure: reject the joint null hypothesis if at least one of t-statistics exceeds 1.96 in absolute value. If t-statistics are independent of each other, what is the probability of rejecting the joint null hypothesis when it is true?

For each residual plot below, decide on whether the usual assumptions: "Y₁ = Bo + B₁2; + €, i = 1,..., n, ₁ independent N(0,0²) random variables" of simple linear regression are valid or not. If some assumptions seem invalid, choose the options(s) which indicate the most obvious departures from the model assumptions. Note: For a small sample, the normality assumption cannot be "proved", but it can be "violated" if there is an extreme residual (outlier). Parta) y-axis has residual, x-axis has x-variable with values 1,2,...,10. (Click on graph to enlarge) Which is/are the best answer(s) for the residual plot (a)? A. linear relation assumption is invalid B. the normality assumption is invalid C. constant variance assumption is invalid D. assumptions seem reasonable E. None of the above

The statsmodels ols() method is used on an exam scores dataset to fit a multiple regression model using Exam4 as the response variable. Exam1, Exam2, and Exam3 are used as predictor variables. The general form of this model is: If the level of significance, alpha, is 0.10, based on the output shown, is Exam1 statistically significant in the multiple regression model shown above? Select one. A text version of this output is available. OLS Regressin Results Dep. Variable: Model: Method: R-squar ed: Adj. R-squared: F-statistic: Prob (F-statistic): Log-Likelihood: AIC: 0.178 0.125 3.329 0.0276 -169.85 347.7 355.4 Exam4 OLS Date: Time: No. Observations: Least Squares Sun, 18 Aug 2019 10:59:12 Df Residuals: of Nodel: Covarianco Тура: 50 46 3 nonr obust BIC: Coef std err P>|t| [0.025 0.975) t Intercept Examl Exam2 Exam3 46.2612 0.1742 0.1462 0.0575 10.969 0.120 0.078 0.053 4.217 1.453 1.873 1.085 0.000 0.153 0.067 0.284 24.181 -0.067 -0.011 -0.049 68.341 0.416 0.303 0.164 Onnibus: 0.886 0.642…

To investigate the relationship between the selling price of a house, yy, in dollars, and the size of the house xx, in square feet, a local builder collected data on a random sample of 120 houses from a certain region. Assume that the conditions for inference for the slope of a regression line are met. The resulting 95 percent confidence interval for the population slope of the regression line relating price and size is given by (62,99). The local builder claims that the selling price of houses from the region increases by $104 for every extra square foot of space in the house. Which of the following best describes the conclusion that can be reached about this claim based on the confidence interval?   A)The claim is supported by the interval, since the interval does not contain the value 0.   B)The claim is supported by the interval, since all values in the interval are positive.   C)The claim is supported by the interval, since the interval does not contain the…

A Simple Linear Regression (SLR) was performed where the monthly Revenue ("Rev", the y-variable) was regressed on the monthly Advertising Expenditures ("Expend", the x-variable). Excel was used to construct the 98% Confidence Interval (CI) estimate of beta subscript 1. The Excel-generated Regression output is provided below: ANOVA   df SS MS F Significance F Regression 1 492.528125 492.528125 10.65525634 0.046980871 Residual 3 138.671875 46.22395833     Total 4 631.2           Coefficients Standard Error  t Stat P-value Lower 95% Upper 95% Lower 98.0% Upper 98.0% Intercept 23.1328125 5.324310936 4.344752359 0.022510469 6.188478833 40.07714617 -1.043301388 47.30892639 Expend 3.1015625 0.950164031 3.264239014 0.046980871 0.077716489 6.125408511 -1.212850033 7.415975033   a. Enter the value of the Left-Hand Endpoint (LHEP) of the 98% Confidence Interval (CI) estimate of beta subscript 1. Round off your answer to the fourth decimal place. The LHEP of the 98% CI for…

The data from exercise 3 follow. xi 2   6 9 13 20 yi 7 18 9 26 23 The estimated regression equation is  = 7.6 + .9x. What is the value of the standard error of the estimate (to 4 decimals)?  What is the value of the t test statistic (to 2 decimals)? What is the p-value? Use Table 1 of Appendix B.Selectless than .01between .01 and .02between .02 and .05between .05 and .10between .10 and .20between .20 and .40greater than .40Item 3 What is your conclusion ( = .05)?SelectConclude a significant relationship exists between x and yCannot conclude a significant relationship exists between x and yItem 4  Use the F test to test for a significant relationship. Use  = .05.Compute the value of the F test statistic (to 2 decimals). What is the p-value?Selectless than .01between .01 and .025between .025 and .05between .05 and .10greater than .10Item 6 What is your conclusion?SelectConclude a significant relationship exists between x and yCannot conclude a significant relationship exists…

Ten observations were provided for a dependent variable y and two independent variables  x1 and x2;  for these data, SST = 15,177.6 and SSR = 14,059.3. (a) Compute  R2.  (Round your answer to three decimal places.) R2 =  (b) Compute  Ra2.  (Round your answer to three decimal places.) Ra2 =  (c) Does the estimated regression equation explain a large amount of the variability in the data? Explain. (For purposes of this exercise, consider an amount large if it is at least 55%. Round your answer to one decimal place.)      , after adjusting for the number of independent variables in the model, we see that  % of the variability in y has been accounted for.