12-6. A regression model is to be developed for predictingthe ability of soil to absorb chemical contaminants. Ten obser-vations have been taken on a soil absorption index (y) and tworegressors: x₁ = amount of extractable iron ore and x₂ = amountof bauxite. We wish to fit the model y = Bo + B₁ x₁ + B₂x₂ + €.Some necessary quantities are:1.17991-7.30982 E-37.3006 E-4(X'X)¹ = -7.30982 E-37.9799 E-5-1.23713 E-4,7.3006 E-4 -1.23713 E-44.6576 E-4220X'y = 36,7689,965(a) Estimate the regression coefficients in the model specified.(b) What is the predicted value of the absorption index y whenx₁ = 200 and x₂ = 50?

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Answered: 12-6. A regression model is to be…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.6: The Inverse Trigonometric Functions

Problem 91E

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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.
Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4
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…
Suppose we want to predict job performance of mechanics based on mechanical aptitude test scores and test scores from personality test that measures conscientiousness. (a) Determine the regression equation. (b) Determine the SSE. Y X1 X2 1 40 25 2 45 20 1 38 30 3 50 30 2 48 28 3 55 30 3 53 34 4 55 36 4 58 32 3 40 34 5 55 38 3 48 28 3 45 30 2 55 36 4 60 34 5 60 38 5 60 42 5 65 38 4 50 34 3 58 38 Where Y is the Performance of the mechanics, X1 is the mechanical aptitude test and X2 is the personality test score that measure conscientiousness.
In a multiple regression problem involving two independent variables, if b1 is computed to be +2.0, it means that the relationship between X1 and Y is significant the estimated mean of Y increases by 2 units for each increase of 1 unit of X1, holding X2 constant. the estimated mean of Y increases by 2 units for each increase of 1 unit of X1, without regard to X2 the estimated mean of Y is 2 when X1 equals zero.
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…
We have been assigned to determine how the total weeklyproduction cost for Widgetco depends on the number ofwidgets produced during the week. The following modelhas been proposed:Y b0 b1X b2X2 b3X3 where X number of widgets produced during the weekand Y total production cost for the week. For 15 weeksof data, we found that SSR 215,475 and SST 229,228.For this model, we obtain the following estimated regressionequation (t-statistics for each coefficient are in parentheses):yˆ 29.7 19.8X 0.39X2 0.005X3(0.78) (0.62) (1.25)a For a 0.10, test H0: bi 0 against Ha: bi 0(i 1, 2, 3).b Determine R2 for this model. How can the high R2value be reconciled with the answer to part (a)?
A fitted linear regression model is (y=10+2x ). If x = 0 and the corresponding observed value of y = 9, the residual at this observation is:
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 .4000
Assume that there is a positive linear correlation between the variable R (return rate in percent of a financial investment) and the variable t (age in years of the investment) given by the regression equation R = 2.3t + 4.8. Without further information, can we assume there is a cause-and-effect relationship between the return rate and the age of the investment? If the investment continues to grow at a constant rate, what is the expected return rate when the investment is 7 years old? If the investment continues to grow at a constant rate, how old is the investment when the return rate is 30%?
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

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