Based on the data shown below, calculate the regression line (each value to two decimal places) y = X 4 5 6 7 8 9 10 y 29.42 29.4 26.18 23.96 22.74 18.62 18.6 X +
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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?The following fictitious table shows kryptonite price, in dollar per gram, t years after 2006. t= Years since 2006 0 1 2 3 4 5 6 7 8 9 10 K= Price 56 51 50 55 58 52 45 43 44 48 51 Make a quartic model of these data. Round the regression parameters to two decimal places.Which of the following does not need to be computed to determine a simple regression line? SSx SP "Y-hat" SSy
- The following data were used in a regression study. Observation 1 2 3 8 5 6 7 8 9 Xi 2 3 4 5 7 7 7 8 9 Yi 4 5 4 7 4 6 9 4 11 Develop an estimated regression equation for these data. (Round your numerical values to two decimal places.)The following data were used in a regression study. Observation 1 2 3 4 5 6 7 8 9 xi 2 3 4 5 7 7 7 8 9 yi 4 5 4 7 4 6 9 5 11 (a) Develop an estimated regression equation for these data. (Round your numerical values to two decimal places.) ŷ =If the standard error of the estimate for a regression model fitted to a large number of paired observations is 1.75, approximately 95% of the residuals would lie within ______. −3.50 and +3.50 −1.75 and +1.75 −0.95 and +0.95 −0.68 and +0.68 −0.97 and +0.97
- BASED ON THIS DATA, what does the r^2 values tell you? and the linear regression line is the information statistically significant?Consider the following hypothetical regression, with FAIL? as a dummy variable for if a business failed in its first year (1=failed, 0=didn’t fail); LOAN is how much money, in thousands of dollars, the business got as a loan when it started; GIG? is a dummy variable for if there was a gig economy job available, such as driving for Lyft (1=available, 0=not available), and COMP is the number of existing competitors the business faced when it started. All variables are statistically significant. FAIL? = 0.63 – 0.01*LOAN – 0.08*GIG? + 0.05*COMP Answer the following: Determine the predicted value of FAIL? if the business had a $30,000 loan, there was no gig economy, and four competitors. In everyday language, what does the estimated value found in A mean? If a business gets an additional six thousand dollars in loans, how would FAIL? change? Give the “punchline” interpretation of the COMP variable: “For every additional competitor…”which of the following regressions represents the strongest negative linear relationship between x and y? (Attached in picture provided)
- Based on the results of the regression, what would be the mose likely conclusion?Based on the data shown below, calculate the regression line (each value to at least two decimal places)y = x + x y 2 19.55 3 18.7 4 19.25 5 17.3 6 19.85 7 18.9 8 18.85 9 18.3 10 15.35 11 16.2 12 18.35 13 14.7Based on the data shown below, calculate the regression line (each value to two decimal places)y = ____ x + ____ x y 3 7.16 4 8.68 5 6.6 6 9.82 7 9.84 8 9.36 9 7.38 10 9.2 11 9.02 12 9.44 13 7.66 14 7.88 15 8.6 16 8.02 17 6.94