An article on estimating 28-day strength of concrete considered regressing y = 28-day standard-cured strength (psi) against x = accelerated strength (psi). Suppose the equation of the true regression line is y == 1,750 + 1.5x.(a) What is the expected value (in pounds per square inch) of 28-day strength when accelerated strength = 2,490 psi?psi(b) By how much can we expect 28-day strength (in pounds per square inch) to change when accelerated strength increases by 1 psi?psi(c) By how much can we expect 28-day strength (in pounds per square inch) to change when accelerated strength increases by 50 psi?psi(d) By how much can we expect 28-day strength (in pounds per square inch) to change when accelerated strength decreases by 50 psi?psi

The given equation of the true regression line is y=1,750+1.5x, where y be the 28-day standard-cured…

Answered: An article on estimating 28-day…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Suppose you ran a regression of AGE predicting INCOME (thousands of dollars). If your estimated line was INCOME = -1.5 + 1.2*AGE + ε, how much more income do you expect to make for every two years you age? (Express your answer in thousands of dollars.)
Data is collected on the distance of several hikes (in miles), along with the amount of time (in minutes) the hike is expected to take. All hikes in the data set are between 0.5 miles and 10 miles long, and the relationship between distance and time is linear and strong. The regression equation to predict time based on distance is as follows: Predicted time = –266 + 31.48 (distance). Suppose we want to use the regression equation to predict the time it takes to complete a particular hike. For which one of the following distances would using the regression equation result in extrapolation? 1 mile 4.5 miles 6.8 miles 9 miles None of the above distances would result in extrapolation.
A particular article presented data on y = tar content (grains/100 ft³) of a gas stream as a function of x₁ = rotor speed (rev/min) and x₂ = gas inlet temperature (°F). The following regression model using X₁, X2, X3 = ×₂² and ×4 = X₁X₂ was suggested. (mean y value) = 86.5 – 0.121x₁ +5.07x2 - 0.0706x3 + 0.001x4 (a) According to this model, what is the mean y value (in grains/100 ft³) if x₁ = 3,400 and x₂ = 55. grains/100 ft³ (b) For this particular model, does it make sense to interpret the value of ₂ as the average change in tar content associated with a 1-degree increase in gas inlet temperature when rotor speed is held constant? Explain. Yes, since there are no other terms involving X2. O Yes, since there are other terms involving X₂. ● No, since there are other terms involving X2. O No, since there are no other terms involving X2.
Consider a dataset with 25 observations and a multiple linear regression model with 4 independent variables. Assume you have estimated the parameters in the model and you find that SSE = 2,389.75 and the SSR = 12,125.25 Find the range that best represents the value of adjusted r-squared, R². (a) R² < 0.80 (b) (c) (d) (e) 0.80 ≤ R² < 0.85 0.85 ≤ R² < 0.90 0.90 ≤ R² < 0.95 0.95 ≤ R²
For a MR model with 4 predictors, we have: SSE 288 and SST = 957 What percentage of the variation in Y is accounted for by its assumed relationship with the predictors?
A trucking company considered a multiple regression model for relating the dependent variable y = total daily travel time for one of its drivers (hours) to the predictors x₁ = distance traveled (miles) and x₂ = the number of deliveries made. Suppose that the model equation is Y = -0.800+ 0.060x₁ +0.900x₂ + e (a) What is the mean value of travel time when distance traveled is 50 miles and four deliveries are made? hr (b) How would you interpret ₁ = 0.060, the coefficient of the predictor x₁? O When the number of deliveries is constant, the average change in travel time associated with a ten-mile (i.e. one unit) increase in distance traveled is 0.060 hours. O The total daily travel time increases by 0.060 hours when the distance traveled increases by 1. O When the number of deliveries is held fixed, the average change in travel time associated with a one-mile (i.e. one unit) increase in distance traveled is 0.060 hours. O The average change in travel time associated with a one-mile (i.e.…
What happened to the standard error of educ after adding KWW to the model? Discuss. Do you agree or disagree with the following statement? “If the log of the dependent variable appears in the regression, changing the unit of measurement of any independent variable affects both the slope and intercept coefficients”. Discuss by providing the resource.
3. A study of beer consumption using the annual data from 1980 -2001 produced the following regression: Y = 0.41 +0.052.X₁; −0.047X2; +0.032X3; −0.018X4i (0.027) (0.011) (0.009) (0.008) (0.009) R² = 0.94 F = 66.58 DW statistic=1.32, figures in the brackets are standard errors Where: Y₁ = Annual aggregate beer consumption in year t (billion pints) X₁₁ = Real disposable income income in year t ($ billions at 2001 prices) X2i = Price of beer in year t (index number with 2001 = 100) X31 Price of wine and sprits in year t (index number with 2001 = 100) = X4₁ = Price of cigarettes in year t (index number 2001 = 100) (a) What is the effect of a change in the price of beer on beer consumption? Does it have the correct sign? Explain. (b) Comment on the signs of the other three coefficients. Are they as expected? (c) Tests the significance of the coefficients on each of the variables Xit i = 1, 2, 3, 4. What assumptions have you made in carrying out these tests? (d) What conclusion do you draw…
If you have a b of 0.56 in a regression equation, what does this mean? For every one-unit increase in x, you get an increase of 0.56 in y r = .31 On average, the variability of real scores around the regression line is 0.56 For every 1 standard deviation increase in x, you get an increase of 0.56 standard deviations in y
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.
Suppose you obtain the following regression model, E[y]=20+53*x +33*x^2. What is the impact of a 63 unit change of x on the expected value of y when x is at its mean of 54?
Suppose you obtain the following regression model, E[y]=20+47*x +88*x^2. What is the impact of a 64 unit change of x on the expected value of y when x is at its mean of 57?

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