For the regression model Yi = B₁ + B₂x₁2 + B3X i3 + Ci what happens if xi3 = 2x₁2 + 3 for all ?? Select one: The statistical inference becomes invalide due to non-normality b. The least-squares estimators are best with the smallest possible variance O c. The regression is not estimable because of exact collinearity d. The least-squares estimators are unbiased a.
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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?Suppose Wesley is a marine biologist who is interested in the relationship between the age and the size of male Dungeness crabs. Wesley collects data on 1,000 crabs and uses the data to develop the following least-squares regression line where ? is the age of the crab in months and ?̂ is the predicted value of ?, the size of the male crab in cm. ?̂=8.2052+0.5693? What is the value of ?̂ when a male crab is 21.7865 months old? Provide your answer with precision to two decimal placeA manufacturer of car batteries claims that the mean lifetime of their battery is 67 months. Thinking that this claim is inflated, graduate students buy a random sample of 72 car batteries from this manufacturer. How should they proceed? a) Perform a hypothesis test of H0:μ=67 versus Ha:μ>67 b) Perform a hypothesis test of H0:μ=67 versus Ha:μ<67 c) Use Simple linear regression
- Suppose Wesley is a marine biologist who is interested in the relationship between the age and the size of male Dungeness crabs. Wesley collects data on 1,000 crabs and uses the data to develop the following least-squares regression line where ? is the age of the crab in months and ?ˆ is the predicted value of ?, the size of the male crab in cm. ?ˆ=8.1312+0.5226? What is the value of ?ˆ when a male crab is 23.0736 months old? Provide your answer with precision to two decimal places. ?ˆ = Interpret the value of ?. The value of ?ˆis the predicted size of a crab when it is 23.0736 months old. the predicted incremental increase in size for every increase in age by 23.0736 months. the predicted number of crabs out of the 1,000 crabs collected that will be 23.0736 months old. the probability that a crab will be 23.0736 months old.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 2In Australia, 16% of the adult population is nearsighted.17 If three Australians are chosen at random, what is the probability that two are nearsighted and one is not? 2.state each of the five assumptions of the classical regression model (OLS) and give an intuitive explanation of the meaning and need for each of them.
- The y-interept bo of a least-squares regression line has a useful interpretation only if the x-values are either all positive or all negative. Determine if the statement is true or false. Why? If the statement is false, rewrite as a true statement.A seafood-sales manager collected data on the maximum daily temperature, T, and the daily revenue from salmon sales, R, using sales receipts for 30 days selected at random. Using the data, the manager conducted a regression analysis and found the least-squares regression line to be Rˆ=126+2.37T. A hypothesis test was conducted to investigate whether there is a linear relationship between maximum daily temperature and the daily revenue from salmon sales. The standard error for the slope of the regression line is SEb1=0.65. Assuming the conditions for inference have been met, which of the following is closest to the value of the test statistic for the hypothesis test? t=0.274 A t=0.65 B t=1.54 C t=3.65 D t=193.85 E9)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
