2.Suppose that in a certain chemical process the reaction time y (hour) isrelated to the temperature x (° F) in the chamber in which the reaction takes placeaccording to the simple linear regression model with equation y= 5 - 0.01x and thestandard deviation o=0.075.a. What is the expected reaction time when temperature is 250° F?b. Suppose that five observations are made independently on reaction time, each onefor a temperature of 250° F. What is the probability that all five times are between2.4 and 2.6 hours?

We have to answer questions based on simple linear regression method.

Answered: 2. Suppose that in a certain chemical…

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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Suppose data is found showing the demand for a product and its price (in dollars) in different market areas where the demand values ranged from 18 to 90. Furthermore, the goal is to use the data to construct a model that will be used to predict the price for the product in terms of its demand. Further, suppose the regression line is found to be y = 23.51535 – 0.09035z The- price for the product when the demand is 160 is: O The average price is 23.51535 - 0.09035(160) = $9.06 anytime the demand is 160 O The average price is 23.51535 - 0.09035(160) = $9.06 for this specific time that the demand is 160 O The price is 23.51535 - 0. 09035(160) = $9 06 anytime the demand is 60 The price is 23.51535 - 0.09035(160) = $9.06 for this specific time that the demand is 60 O The answer cannot be found due to extrapolation
An economist wants to estimate a regression equation relating demand for a product (Y) to its price (X1) and income (X2). It is to be based on 12 years of quarterly data. However, it is known that demand for this product is seasonal; that is, it is higher at certain times of the year than others.a. One possibility for accounting for seasonality is to estimate the modely = β0 + β1x1 + β2x2 + β3x3 + β4x4 + β5x5 + β6x6 + εwhere x3, x4, x5, and x6 are dummy variable values, withx3 = 1 in first quarter of each year, 0 otherwisex4 = 1 in second quarter of each year, 0 otherwisex5 = 1 in third quarter of each year, 0 otherwisex6 = 1 in fourth quarter of each year, 0 otherwiseExplain why this model cannot be estimated by least squares.b. For a model that can be estimated is as follows:y = β0 + β1x1 + β2x2 + β3x3 + β4x4 + β5x5 + εinterpret the coefficients on the dummy variables in the model.
The estimated regression equation for a model involving two independent variables and 10 observations follows. ŷ = 32.4394 + 0.5695x1 + 0.7347x2 a. Interpret b1 and b2 in this estimated regression equation (to 4 decimals). b. Estimate y when x1 = 180 and x2 = 310 (to 3 decimals).
The owner of a movie theater company used multiple regression analysis to predict gross revenue (y) as a function of television advertising (x1) and newspaper advertising (x2). The estimated regression equation was ŷ = 82.4 + 2.23x1 + 1.40x2. The computer solution, based on a sample of eight weeks, provided SST = 25.5 and SSR = 23.495.(Note: SST = SS yy ) (a)Compute and interpret R2 and Ra2. (Round your answers to three decimal places.) The proportion of the variability in the dependent variable that can be explained by the estimated multiple regression equation is (??) . Adjusting for the number of independent variables in the model, the proportion of the variability in the dependent variable that can be explained by the estimated multiple regression equation is (??) . (b)When television advertising was the only independent variable, R2 = 0.653 and Ra2 = 0.595. Is the multiple regression model more preferable over the simple regression model? Explain. Multiple…
An estimated regression equation is In (ŷ) =-1+ 2x. Then we can forecast: O a = 2.72 if x = 1. %3D O b. x = 1 if ŷ = 2.72. Oc ŷ = 0.05 if x = 1. %3D %3D Od x = 1 if ŷ = 1. eŷ = 1 if x = 1.
An independent researcher is interested in studying the factors that affects the educational attainment of an individual (Y). For her study she chooses educational attainment of the individual's mother (X,) and the annual income of the individual's family (X,) as regressors. The researcher randomly selects a sample of 280 individuals and estimates the following regression function: Y = 8.00 + 1.74X, +2.12X2 (0.76) (1.98) She wants to test whether or not a change in (X,) significantly affects (Y) keeping the annual income of the individual's family constant. The t-statistic for testing the hypothesis Ho: B1 = 0 vs. H1 B1 0 will be (Round your answer to two decimal places.) If the researcher uses a 5% significance level, we the null hypothesis. She now includes the educational attainment of the individual's father (X) as the third regressor in the regression equation. The newly estimated regression equation is: Y, = 8.51 + 0 83X, +2.01X2 + 2.12X3. (2.20) (2.14) (1.57) With the revised…
A researcher is interested in finding out the factors which determined the yearly spending on family outings last year (Y, measured in dollars). She compiles data on the number of members in a family (X,), the annual income of the family (X,), and the number of times the family went out on an outing in the last year (X). She collects data from 152 families and estimates the following regression: Y = 120.45 + 1.12X, + 2.12X2 + 1.98X3 Suppose B1. B2, B3, denote the population slope coefficients of X, X2, and X3, respectively The researcher wants to check if neither X, nor X, have a significant effect on Y or at least one of them has a significant effect, keeping X3 constant. She calculates the value of the F-statistic for the test with the two restrictions (Ho: B, = 0, B2 = 0 vs. H B, 0 and/or Bz 0) to be 3.00. The p-value for the test will be (Round your answer to two decimal places.) At the 10% significance level, we will the null hypothesis. reject fail to reject Enter your answer in…
The following estimated regression model was developed relating yearly income (y in $1000s) of 30 individuals with their age (x1) and their gender (x2) (0 if male and 1 if female).ŷ = 30 + 0.7x1 + 3x2Also provided are SST = 1200 and SSE = 384.The yearly income of a 24-year-old female individual is
Data was gathered from a random sample of young mothers between the ages of 15 and 19 years, and the relationship between the mother's age (measured in years) and the baby's birth weight (measured in grams) was observed to be linear, with r= 0.88. Further, the regression equation to predict a baby's birth welght based on the mother's age was found to be: Predicted birth weight = -1163.45 + 245.15(age). Based on this information, which one of the following statements is incorrect? O The predicted birth weight for a baby whose mother is 15 years old is 4840.7 grams. O If weight was measured in pounds instead of grams, the value of rwould still be 0.88. O If we switch the variables so that age is the response variable and birth weight is the explanatory variable, r would still be 0,88. O If a mother's age is 25 years, we would not want to use the regression equation to predict the baby's birth weight since this would be considered extrapolation. O Becauseris 0.88, we would consider the…
Calculate the estimate of σε What is the estimated resting heart rate for someone who is a smoker (Smoke=1) and exercises 1 hour a day (Exercise=1)?
A researcher believes that there is a linear association between the level of potassiumcontent (y) in milligrams and the amount of fiber (x) in grams in cereal. The regression line forthe data is computed to be: ŷ = 36+27x rate. It was also computed that r = .62 b. If a cereal has 4 grams of fiber and a potassium content of 160 milligrams, what is thevalue of the residual?
1. You will obtain regression estimates predicting Attendance from the number of Flyers posted around town and whether the flyers were posted in Color. Assume standard regression assumptions hold. 1a. Give the regression estimate assuming the model: Attendance = β0 + β1*Flyers + β2*Color. (Round your answers to 4 decimal places.) Attendance = +. * (Flyers) + *(Color) 1b. How many people are expected to attend if the band posted 80 flyers printed in color around town? (Round final answers to 2 decimal places.) Predicted Attendance: 1c. At the 5% level, would you recommend that the band post flyers printed in color when advertising for their show (provided that the increase in cost of printing in color is negligible)? multiple choice 1 Yes, since we reject the relevant H0. Yes, since we do not reject the relevant H0. No, since we reject the relevant H0

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