Xdbar = (O S = D D O \130 D 120/ S-1 = (0 D O ? D ? \30 Q (p)? Sample Size (n)? Subgroup (m)? Alpha=CC01 F(alpha,p,mn-m-p+1)?. . 1 3 4 5 6 9 10 11 12 13 58 60 50 54 63 53 42 55 46 50 49 57 58 32 33 27 31 38 30 20 31 25 29 27 30 33 2.
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- If in a multivariate regression model with significant F-value, all the estimated parameters have computed-t values less than 1, then the model is likely to have _____. Select one: a. partial correlation for each regressor is insignificant b. some or all the regressors are linearly dependent c. a problem of multicollinearity d. all of the aboveQ3 - Returns on stocks X and Y are listed below: Period 1 2 3 4 5 6 7Stock X 3% -2% 9% 6% -1% -4% 11%Stock Y 1% -4% 7% 12% 3% -2% -1% Consider a portfolio of 20% stock X and 80% stock Y. What is the (population) variance of portfolio returns? Please round your answer to six decimal places.Q3 - Returns on stocks X and Y are listed below: Period 1 2 3 4 5 6 7Stock X 5% 6% -2% -4% 6% 10% 7%Stock Y 1% -3% 6% 3% 12% 7% -5% Consider a portfolio of 40% stock X and 60% stock Y. What is the (population) variance of portfolio returns?Please round your answer to six decimal places.
- E3 a) Distinguish between the Population Regression Function (PRF) and the Sample Regression Function (SRF) using appropriate formula and specifications for each function. b) Outline the Gauss-Markov assumptions associated with the Classical Linear Regression Model (CLRM) and discuss their significance. State any additional assumption that is required for hypotheses testing. Ensure to elaborate on BLUE properties of OLS estimators.Engro group, who recently sold its Engro foods start-up for a multi-million-rupees sum, is looking for another investment for fresh capital. It is considering an investment in coal (X) and solar (Y) power plant. For that they had a collected data on 5 different characteristics. Amanda has applied k-means clustering to this data for k = 2. Given the following data: Table 5.1 Observations X Y 1 20 18 2 8 20 3 36 26 4 22 12 5 14 4 Visually represent the clusters of both parts9)Suppose that Y is normal and we have three explanatory unknowns which are also normal, and we have an independent random sample of 11 members of the population, where for each member, the value of Y as well as the values of the three explanatory unknowns were observed. The data is entered into a computer using linear regression software and the output summary tells us that R-square is 0.79, the linear model coefficient of the first explanatory unknown is 7 with standard error estimate 2.5, the coefficient for the second explanatory unknown is 11 with standard error 2, and the coefficient for the third explanatory unknown is 15 with standard error 4. The regression intercept is reported as 28. The sum of squares in regression (SSR) is reported as 79000 and the sum of squared errors (SSE) is 21000. From this information, what is the adjusted R-square? .8 .7 NONE OF THE OTHERS .6 .5
- 17) Suppose that Y is normal and we have three explanatory unknowns which are also normal, and we have an independent random sample of 41 members of the population, where for each member, the value of Y as well as the values of the three explanatory unknowns were observed. The data is entered into a computer using linear regression software and the output summary tells us that R-square is 0.9, the linear model coefficient of the first explanatory unknown is 7 with standard error estimate 2.5, the coefficient for the second explanatory unknown is 11 with standard error 2, and the coefficient for the third explanatory unknown is 15 with standard error 4. The regression intercept is reported as 28. The sum of squares in regression (SSR) is reported as 90000 and the sum of squared errors (SSE) is 10000. From this information, what is the number of degrees of freedom for the t-distribution used to compute critical values for hypothesis tests and confidence intervals for the individual…9) The following results are from a regression where the dependent variable is GRADUATION RATE and the independent variables are % OF CLASSES UNDER 20, % OF CLASSES OF 50 OR MORE, STUDENT/FACULTY RATIO, ACCEPTANCE RATE, 1ST YEAR STUDENTS IN TOP 10% OF HS CLASS. The data were split into 2 samples and the following regression results were obtained from the split data. a) What is heteroscedasticity? (b) Why is heteroscedasticity a problem? c) Based on a comparison of the two sets of output, does it appear that there is heteroscedasticity in the data set? Explain. Be sure to write down your null and alternative hypothesis, calculate the test statistic, and find your critical value (test at the 5% level of significance).8)Suppose that Y is normal and we have three explanatory unknowns which are also normal, and we have an independent random sample of 11 members of the population, where for each member, the value of Y as well as the values of the three explanatory unknowns were observed. The data is entered into a computer using linear regression software and the output summary tells us that R-square is 0.86, the linear model coefficient of the first explanatory unknown is 7 with standard error estimate 2.5, the coefficient for the second explanatory unknown is 11 with standard error 2, and the coefficient for the third explanatory unknown is 15 with standard error 4. The regression intercept is reported as 28. The sum of squares in regression (SSR) is reported as 86000 and the sum of squared errors (SSE) is 14000. From this information, what is MSE/MST? .5000 NONE OF THE OTHERS .2000 .3000 .4000
- 3- Heteroskedasticity refers to the residuals from a regression model Select one:Being linearBeing independentHaving a constant varianceHaving time-dependent varianceClear my choiceA scatterplot of student height, in inches, versus corresponding arm span length, in inches, is shown below. One of the points in the graph is labeled A. If the point labeled A is removed, which of the following statements would be true? The slope of the least squares regression line is unchanged and the correlation coefficient increases. The slope of the least squares regression line is unchanged and the correlation coefficient decreases. The slope of the least squares regression line increases and the correlation coefficient increases. The slope of the least squares regression line increases and the correlation coefficient decreases. The slope of the least squares regression line decreases and the correlation coefficient increases.2. An article in the Tappi Journal (March, 1986) presented data on green liquor Na2S concentration (in grams per liter) and paper machine production (in tons per day). The data (read from a graph) are shown as follows: (a) Fit a simple linear regression model with y green liquor Na2S concentration and x production. Draw a scatter diagram of the data and the resulting least squares fitted model.(b) Find the fitted value of y corresponding to x = 910 and the associated residual.
