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- Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4The 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.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?
- Use the following linear regression equation to answer the questions. x1 = 1.5 + 3.6x2 – 7.8x3 + 1.8x4 (c) If x2 = 10, x3 = 7, and x4 = 7, what is the predicted value for x1? (Use 1 decimal place.) answer: -4.5 Suppose x3 and x4 were held at fixed but arbitrary values and x2 increased by 1 unit. What would be the corresponding change in x1? answer:3.6 Suppose x2 increased by 2 units. What would be the expected change in x1? answer: 7.2 Suppose x2 decreased by 4 units. What would be the expected change in x1? (e) Suppose that n = 13 data points were used to construct the given regression equation and that the standard error for the coefficient of x2 is 0.461. Construct a 95% confidence interval for the coefficient of x2. (Use 2 decimal places.) lower limit upper limit (f) Using the information of part (e) and level of significance 1%, test the claim that the coefficient of x2 is different from zero. (Use 2 decimal places.) t 7.81 t critical ±Use the following linear regression equation to answer the questions. x3 = −17.3 + 4.1x1 + 9.6x4 − 1.6x7 Suppose x1 and x7 were held at fixed but arbitrary values. a) If x4 increased by 1 unit, what would we expect the corresponding change in x3 to be? b) If x4 increased by 3 units, what would be the corresponding expected change in x3? c) If x4 decreased by 2 units, what would we expect for the corresponding change in x3?Use the following linear regression equation to answer the questions. x3 = −15.4 + 4.0x1 + 8.2x4 − 1.2x7 (d)Suppose x1 and x7 were held at fixed but arbitrary values.If x4 increased by 1 unit, what would we expect the corresponding change in x3 to be?If x4 increased by 3 units, what would be the corresponding expected change in x3?If x4 decreased by 2 units, what would we expect for the corresponding change in x3?(e) Suppose that n = 14 data points were used to construct the given regression equation and that the standard error for the coefficient of x4 is 0.917. Construct a 90% confidence interval for the coefficient of x4. (Round your answers to two decimal places.) lower limit upper limit (f) Using the information of part (e) and level of significance 5%, test the claim that the coefficient of x4 is different from zero. (Round your answers to two decimal places.) t = t critical = ±
- Use the following linear regression equation to answer the questions. X1=1.9+3.6x2-7.5x3+2.1x4 a) which number is the constant term? List the coefficients with their corresponding explanatory variables. constant=x2 coefficient =x3 coefficient =x4 coefficient =b) If x3 and x4 were held at fixed but arbitrary values and x2 increased by 1 unit. What would be the corresponding change in x1? suppose x2 increased by 2 units. What would be the expected change in x1? suppose x2 decreased by 4 units. What would be the expected change in x1? c) Suppose that n=13 data points were used to construct the given regression equation and that the standard error for the coefficient of x2 is 0.433. Construct a 95% confidence interval for the coefficient of x2. (Use 2 decimal places)Use the following linear regression equation to answer the questions. x1 = 2.0 + 3.6x2 – 7.8x3 + 2.1x4 a) Which variables are the explanatory variables? (Select all that apply.) x3 x1 x2 x4 (b) Which number is the constant term? List the coefficients with their corresponding explanatory variables. constant _____ x2 coefficient _____ x3 coefficient _____ x4 coefficient ______ (c) If x2 = 9, x3 = 3, and x4 = 6, what is the predicted value for x1? (Use 1 decimal place.)Use the following linear regression equation to answer the questions. x1 = 1.5 + 3.6x2 – 7.8x3 + 1.8x4 Which variables are the explanatory variables? (Select all that apply.) x4x3x2x1 (c) If x2 = 10, x3 = 7, and x4 = 7, what is the predicted value for x1? (Use 1 decimal place.)Suppose x3 and x4 were held at fixed but arbitrary values and x2 increased by 1 unit. What would be the corresponding change in x1?Suppose x2 increased by 2 units. What would be the expected change in x1?Suppose x2 decreased by 4 units. What would be the expected change in x1?(e) Suppose that n = 13 data points were used to construct the given regression equation and that the standard error for the coefficient of x2 is 0.461. Construct a 95% confidence interval for the coefficient of x2. (Use 2 decimal places.) lower limit upper limit (f) Using the information of part (e) and level of significance 1%, test the claim that the coefficient of x2 is different from zero. (Use 2 decimal places.) t t…
- Use the following linear regression equation to answer the questions. x3 = −15.4 + 4.0x1 + 8.2x4 − 1.2x (a) Which variables are the explanatory variables? (Select all that apply.) x4 x3 x7 x1 (b) Which number is the constant term? List the coefficients with their corresponding explanatory variables. constant x1 coefficient x4 coefficient x7 coefficient (c) If x1 = 9, x4 = -5, and x7 = 4, what is the predicted value for x3? (Round your answer to one decimal place.)x3 =Suppose that in a certain chemical process the reaction time y (hr) is related to the temperature (°F) in the chamber in which the reaction takes place according to the simple linear regression model with equation y = 5.10 − 0.01x and ? = 0.07. (a) What is the expected change in reaction time for a 1°F increase in temperature? For a 12°F increase in temperature? 1°F increase hr 12°F increase hr (b) What is the expected reaction time when temperature is 190°F? When temperature is 240°F? 190°F hr 240°F hr (c) Suppose five observations are made independently on reaction time, each one for a temperature of 240°F. What is the probability that all five times are between 2.58 and 2.82 hours? (Round your answer to four decimal places.)(d) What is the probability that two independently observed reaction times for temperatures 1° apart are such that the time at the higher temperature exceeds the time at the lower temperature? (Round your answer to four decimal…5. In simple linear regression: a.The larger the coefficient of determination, then the more precisely the y variable can be predicted from the x variable. b.The larger the coefficient of determination, then the less precisely the y variable can be predicted from the x variable. c.Neither of the above. d.Both of the above.
