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?

Answered: Image /qna-images/answer/efca2537-964a-4a2f-bbd5-9715285203ce.jpg

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

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, and range from heights of 132 to 190 cm and weights of 41 to 150 kg. Let the predictor variable x be the first variable given. The 100 paired measurements yield x=167.40 cm, y=81.39 kg, r=0.172, P-value=0.087, and y=−103+1.02x. Find the best predicted value of y (weight) given an adult male who is 143 cm tall. Use a 0.10 significance level. The best predicted value of y for an adult male who is 143 cm tall is enter your response here kg. (Round to two decimal places as needed.)
1. We wish to determine a regression equation that relates the length of an infant (in cm) to age (in days), gender and weight at birth (in kg). Below is portion of the regression analysis derived using a software. *Note: under the gender variable: male and female categories are assigned a value of 1 and 0, respectively. Source S df Coef. Std. Err. 316.8866 3 Residual 71.4734 Model 0.4798 0.0980 age weight gender intercept 8 0.4020 1.0454 1.3113 1.9591 19.53 7.7829 a. What is the sample size for this problem? b. Write the estimated regression equation, interpret each slope coefficients, use the proper unit of measurement. c. Test for significance of the Bage, Bweight, and ßgender at the 99% confidence level. d. From (b) which parameter/s islare statistically significant. e. Test whether or not there is a significant relationship between the infant's length and the independent variables. Use a .01 level of significance. Use only the critical value approach. f. Provide the Coefficient of…
Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, and range from heights of 134 to 194 cm and weights of 39 to 150 kg. Let the predictor variable x be the first variable given. The 100 paired measurements yield x=167.78 cm, y=81.45 kg, r=0.372, P-value=0.000, and y=−101+1.11x. Find the best predicted value of y (weight) given an adult male who is 145 cm tall. Use a 0.05 significance level. The best predicted value of y for an adult male who is 145 cm tall is enter your response here kg. (Round to two decimal places as needed.)
Q1: The data points below are related to a chemi-thermo-mechanical pulp from mixed density hardwoods. They relate Y (specific surface area of the fibres in cm/g) to the % NaOH (sodium hydroxide) used as a pretreatment chemical and the treatment time (min) for different batches of pulp. The variables are present at three different levels. In this case, it is preferred (for reasons that we will discuss later in the course) to code the levels as shown in the last two columns of the table below, designated by Xı and X2. Y SODIUM ΤΙME Xi X2 HYDROXIDE 5.95 3 30 -1 5.60 3 60 -1 5.44 3 90 -1 1 6.22 9. 30 -1 5.85 9 60 5.61 9. 90 1 8.36 15 30 1 -1 7.30 15 60 1 6.43 15 90 1 1 a. Using the variables Y, X1 and X2 (not actual time and sodium hydroxide! You will see why later!), fit the following multiple linear regression model to the data: (Model A) Y = (b0) + (b1) X1 + (b2) X2; subsequently, estimate the parameters and examine the residual plot (residuals vs Y hat). What does this residual plot…
Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, and range from heights of 133 to 188 cm and weights of 40 to 150 kg. Let the predictor variable x be the first variable given. The 100 paired measurements yield x=167.80 cm, y=81.36 kg, r=0.286, P-value=0.004, and y=−108+1.19x. Find the best predicted value of y (weight) given an adult male who is 138 cm tall. Use a 0.10 significance level.
1. Model 1: OLS, using observations 1-706 Dependent variable: RST Coefficient Std. Error t-ratio p-value const 3586.38 38.9124 92.17 <0.0001 *** TOTWRK −0.150746 0.0167403 −9.005 <0.0001 *** Mean dependent var 3266.356 S.D. dependent var 444.4134 Sum squared resid 1.25e+08 S.E. of regression 421.1357 R-squared 0.103287 Adjusted R-squared 0.102014 F(1, 704) 81.08987 P-value(F) 1.99e-1810538.19 Log-likelihood −5267.096 Akaike criterion 10538.19 Schwarz criterion 10547.31 Hannan-Quinn 10541.71 RSTi =3586.38−0.150746 x TOTWRKi , R2=0.103287,SER=421.1357 (38.9124) (0.0167403) Question? could you please help with this question below. 3) By observing the GRETL output in Part (1) above, provide a detailed explanation of the coefficient of determination. Based on your analysis, is this a good model? Why or why not?
Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, and range from heights of 139 to 189 cm and weights of 39 to 150 kg. Let the predictor variable x be the first variable given. The 100 paired measurements yield x=167.70 cm, y=81.43 kg, r=0.324, P-value=0.001, and y=−101+1.06x. Find the best predicted value of y (weight) given an adult male who is 151 cm tall. Use a 0.10 significance level. Question content area bottom Part 1 The best predicted value of y for an adult male who is 151 cm tall is enter your response here kg. (Round to two decimal places as needed.)
An investigation into the relationship between an adolescent mother's age x in years and the birth weight y of her baby in grams yielded the regression equation y= - 1163.45 + 245.15x as well as r = .88369, r2= .78091, SSE = 337212.45, and s= 205.30844 1) What is the predicted birth weight for a baby brn to a 17 year old woman? 2) What is the propotion of the variability in the weights of babies born to adolescent mothers that is accounted for by the mother's age? 3) For every additional year in the mother's age that mean birth weight of the baby? (a) increases by about 245g (b) decreases by about 245g (c) increases by about 1163g (d) increases by about 1163g (e) changes by an amount that cannot be determined from the information given.
An engineer measures the peak current (in microamps) when a solution containing an amount of nickel (in parts per 10°) is added to a buffer. The experiment was repeated for eleven different values of nickel solutions. A scatterplot showing the data is given below: Peak Current in Eleven Buffers with Added Nickel Solutio 60 120 140 100 Amount of nickel (pp million) Suppose a regression line was added to the plot above. If an additional measurement had been taken with the nickel of 62 parts per 10 and a peak current of 0.38 microamps, adding this observation would: O A. increase the intercept, decrease the slope. OB. increase the intercept, increase the slope. C. decrease the intercept, increase the slope. OD. decrease the intercept, decrease the slope. E. not affect the regression line.
The estimated regression equation for a model involving two independent variables and 10 observations follows. ý = 22.1370 + 0.5303Xq + 0.4920X2 (a) Interpret b₁ in this estimated regression equation. O b₁ = 0.5303 is an estimate of the change in y corresponding to a 1 unit change in x₂ when x₁ is held constant. O b₁ = 0.5303 is an estimate of the change in y corresponding to a 1 unit change in x₁ when X₂ is held constant. O b₁ = 22.1370 is an estimate of the change in y corresponding to a 1 unit change in x₁ when x₂ is held constant. O b₁ = 0.4920 is an estimate of the change in y corresponding to a 1 unit change in x₂ when x₁ is held constant. O b₂ = 0.4920 is an estimate of the change in y corresponding to a 1 unit change in x₁ when x₂ is held constant. Interpret b₂ in this estimated regression equation. O b₂ = 0.4920 is an estimate of the change in y corresponding to a 1 unit change in x₂ when x₁ is held constant. O b₂ = 22.1370 is an estimate of the change in y corresponding to a…
18. Because ethanol contains less energy than gasoline, a researcher wants to determine if the mileage of a car (y) is affected by the percent ethanol in the gasoline (x). The true population regression line relating the mean mileage y for a given ethanol content x (in percent) is μy|x = β0 + β1x. In a controlled environment, the mileage of a car is recorded when refueled 7 times using between 0% and 10% ethanol. The least squares regression line was found to be yˆ = βˆ0 + βˆ1x = 32.96 − 0.250x. We wish to test H0 : β1 = 0 versus Ha : β1 < 0 at the α = 0.05 significance level (i.e. we want to determine if the addition of ethanol significantly decreases mean gas mileage). What is the p−value for this test? What is your conclusion? Note: s?e(βˆ1) = 0.0485. Which of the following is/are true? (A) In reference to question (18), it would be appropriate to approximate the mean mileage when the car is using 85% ethanol (B) In reference to question (18), a 95% confidence interval for β1…
4.5. After fitting the regression model, y= Bo + Bix1 + Brx2+ B3x3+€ on 15 cases, it is found that the mean square error s? =3 and 0.5 0.3 0.2 0.6 0.3 6.0 0.5 0.4 (X'X)-' = 0.2 0.5 0.2 0.7 0.6 0.4 0.7 3.0 Find a. The estimate of V (ß1). b. The estimate of Cov(ß¡, ß3). c. The estimate of Corr(ß1, ß3). d. The estimate of V (ß¡ – B3).

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