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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 linear regression model based on a random sample of 36 observations on the response variable and 4 predictors has a multiple coefficient of determination equal to 0.697. What is the value of the adjusted multiple coefficient of determination?17. When the heights (in inches) and shoe lengths (also in inches) were measured for a large random sample of individuals, it was found that r = 0.89, and a regression equation was constructed in order to further explore the relationship between shoe length and height, with height being the response variable. From this information, what can we conclude? 1. The regression equation relating shoe length to height must have a positive intercept. 2. Approximately 89% of the variability in height can be explained by the regression equation. 3. Because the value of r is less than 1, we should characterize this relationship as being weak. 4. The regression equation relating shoe length to height must have a slope equal to 0.89. 5. The correlation coefficient should have no units.
- 4. In multiple regression, why do we prefer our IVs to be uncorrelated with each other (i.e., we want to be 0)?Suppose the simple linear regression model, Yi = β0 + β1 xi + Ei, is used to explain the relationship between x and y. A random sample of n = 12 values for the explanatory variable (x) was selected and the corresponding values of the response variable (y) were observed. A summary of the statistics is presented in the photo attached. Let b1 denote the least squares estimator of the slope coefficient, β1. What is the value of b1?In estimating the regression in the previous problem (#2), you are concerned that the t-statistics may be inflated because of serial correlation. You compute the DW statistic at 0.724 for the regression. Compute the sample correlation between the regression residuals from one period and those from the previous period. Perform a statistical test at the level to see if there is serial correlation. If you are using the table in the textbook, assume that the critical values of the DW statistic for 214 observations are about 0.11 higher than the critical values for 100 observations.
- If you have a b of 0.56 in a regression equation, what does this mean? For every one-unit increase in x, you get an increase of 0.56 in y r = .31 On average, the variability of real scores around the regression line is 0.56 For every 1 standard deviation increase in x, you get an increase of 0.56 standard deviations in yHaving the variation data regression line r=0.931 and the calculated coefficient of determination of 0.867.. And explained variation of the data of 86.7%.. About the unexplained variation? [ ] % of the variation is unexplained and is due to other factors or to sampling error. (Round to one decimal place as needed.)A physician wants to test if temperature has an effect on heart rate. In order to do this, she compares the heart rates in beats per minute of several random volunteers after a period of time in a room with a temperature of 50∘F and after a period of time in a room with a temperature of 75∘F. Suppose that data were collected for a random sample of 11 volunteers, where each difference is calculated by subtracting the heart rate in beats per minute in the 50∘F room from the heart rate in beats per minute in the 75∘F room. Assume that the populations are normally distributed. The physician uses the alternative hypothesis Ha:μd≠0. Suppose the test statistic t is computed as t≈5.627, which has 10 degrees of freedom. What range contains the p-value?
- 17. When the heights (in inches) and shoe lengths (also in inches) were measured for a large random sample of individuals, it was found that r = 0.89, and a regression equation was constructed in order to further explore the relationship between shoe length and height, with height being the response variable. From this information, what can we conclude? 1. Approximately 89% of the variability in height can be explained by the regression equation. 2. The regression equation relating shoe length to height might have a negative intercept. 3. Because the value of r is less than 1, we should characterize this relationship as being weak. 4.The correlation coefficient should have the units of “inches.” 5. The regression equation relating shoe length to height must have a slope equal to 0.89.Suppose that the general fertility rate, g f rt , is following an AR(1) process shown in the image below A) if y1<1, what is the expression for the mean and variance of g f t rt showing any assumptions that were made . b) suppose that Var (€|gfrt-1)= as shown in the image below. explain why you may not obtain a best linear unbiased estimator of y0 and y1 by estimating (3) using OLS.In a certain jurisdiction, all students in Grade Three are required to take a standardized test to evaluate their math comprehension skills.The file contains these data resulting from a random sample of n=30 schools within this jurisdiction. From these data you wish to estimate the model Yi=β0+β1Xi+ei where Xi is the percentage of Grade Three students in School i who live below the poverty line and Yi is the average mathematics comprehension score for all Grade Three students in the same school, School i. The observed data for the X variable is labled perbelowpoverty and the observed data for the Y variable is labeled mathscore in the file.Import (either hand type or load the file) data into R Studio, then answer the following questions based on the data.(a) Create a scatterplot of the data. What can you say about the nature of the relationship between the percentage of Grade Three students living below the poverty line in a certain school and the school's average Grade Three…