2. Here is the equation of the list squares of regression line: y=31.9-0.304x. Sample size is 13. S= 3.667. S. -13.033. = 58.23 (a) Do the test of hypothesis: H,: B = 0; Hạ:B +0 What is SE,? What is the t value? What is the degree of freedom? What is the p-value? Should the null hypothesis be rejected if the significance level is a =0.05? Continue or not? ( Hint: Consider the formula of S. (b) Ifx 60, Find the 95% confidence interval for the single predicted value ŷ.
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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?A set of n = 15 pairs of X and Y values has a correlation of r = +0.80 with SSY = 75, and the regression equation for predicting Y is computed. Find the standard error of estimate for the regression equation. How big would the standard error be if the sample size were n = 30.What is the effect of this violation on the regression model? "The number of observations n is less than or equal to the number of parameters to be estimated"
- The best predicted crash fatality rate for a year in which there are 525 metric tons of lemon imports is ____________ fatalities per 100,000 population. Is the prediction worthwhile? A.Since common sense suggests there should not be much of a relationship between the two variables, the prediction does not make much sense. B. Since the sample size is small, the prediction is not appropriate. C. Since all of the requirements for finding the equation of the regression line are met, the prediction is worthwhile. D.Since there appears to be an outlier, the prediction is not appropriate.If a new independent variable is added to a regression equation, the adjusted R2 increases only if the absolute value of the t-statistic of the new variable is greater than one. Group of answer choices True False.9)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
- Mr. James, president of Daniel-James Financial Services, believes that there is a relationship between the number of client contacts and the dollar amount of sales. To document this assertion, he gathered the following information from a sample of clients for the last month. Let X represent the number of times that the client was contacted and Y represent the valye of sales ($1000) for each client sampled. Number of Contacts (X) Sales ($1000) 14 24 12 14 20 28 16 30 23 30 a) Compute the regression equation for client contacts and sales. Interpret the slope and intercept parameters.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…5) The following results are from data where the dependent variable is SALARY, the independent variables are AGE, EDUCATION, and FEMALE which is a dummy variable = 1 for females and = 0 for males. b) How much of the variation in income is explained by the regressors? c) What is the standard error of the error term in the regression equation? d) Are any of the explanatory (independent) variables significant at the 10% level of significance? How do you know?
- 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 .4000The average midterm score in a large statistics class was 70 with an SD of 10. The average final score in the same class was 65 with an SD of 15. The correlation coefficient between midterm and final scores was r=0.6. Using the regression line, we predict the final score of a student with a midterm score of 60 to be , but this prediction is likely to be off by about . Fill in the blanks, rounding each answer to one decimal point.