The following estimated regression equation was developed for a model involving two independent variables.ý = 40.7 + 8.63x, + 2.71.x,After x 2 was dropped from the model, the least squares method was used to obtain an estimated regression equation involving onlyX 1 as an independent variable.ŷ = 42.0 + 9.01xa. In the two independent variable case, the coefficient x 1 represents the expected change in Select v corresponding to a one unitincrease in Select v when Select v is held constant.In the single independent variable case, the coefficient x 1 represents the expected change in Select v corresponding to a oneunit increase in Select vb. Could multicollinearity explain why the coefficient of x 1 differs in the two models? Assume that x1 and x2 are correlated.Select

The dependent variable is y. The independent variables are x1 and x2. This is multiple regression…

Answered: The following estimated regression…

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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A company that manufactures computer chips wants to use a multiple regression model to study the effect that 3 different variables have on y, the total daily production cost (in thousands of dollars). Let B,, B,, and B, denote the coefficients of the 3 variables in this model. Using 22 observations on each of the variables, the software program used to find the estimated regression model reports that the total sum of squares (SST) is 485.84 and the regression sum of squares (SSR) is 229.91. Using a significance level of 0.10, can you conclude that at least one of the independent variables in the model provides useful (i.e., statistically significant) information for predicting daily production costs? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. (a) State the null hypothesis H, for the test. Note that the alternative hypothesis H, is given. H, :0 H, : at least one of the independent variables is useful…
Suppose Wesley is a marine biologist who is interested in the relationship between the age and the size of male Dungeness crabs. Wesley collects data on 1,000 crabs and uses the data to develop the following least-squares regression line where X is the age of the crab in months and Y is the predicted value of Y, the size of the male crab in cm. Y = 8.2052 + 0.5693X What is the value of Ý when a male crab is 21.7865 months old? Provide your answer with precision to two decimal places. Interpret the value of Ý. The value of Ý is the probability that a crab will be 21.7865 months old. the predicted number of crabs out of the 1,000 crabs collected that will be 21.7865 months old. the predicted incremental increase in size for every increase in age by 21.7865 months. the predicted size of a crab when it is 21.7865 months old.
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FRQ 2 Professional basketball teams have 11 players per team. Salary is dependent upon their scoring average, measured in points per game. A least-squares regression line that describes the relationship between scoring average and salary for one professional basketball team is ŷ = 2,671,134.68 +684,663.08x, where x is the player's scoring average and y is the player's salary. The residuals for this regression are given in the graph below. Residual $20,000,000 $15,000,000 $10,000,000 $5,000,000 $0 -$5,000,000 -$10,000,000 -$15,000,000 4 ITS % 6 MacBook Pro ● 8 ● ● ● 10 12 14 Scoring Average (Points per Game) Is a line an appropriate model to use for these data? What information tells you this? b) What is the value of the slope of the least-squares regression line? Interpret the slope in the context of this problem. c) What is the predicted salary of the basketball player with 10.9 points per game? d) Approximate the actual salary of the basketball player with 10.9 points per game. 16 tv…
Biologist Theodore Garland, Jr. studied the relationship between running speeds and morphology of 49 species of cursorial mammals (mammals adapted to or specialized for running). One of the relationships he investigated was maximal sprint speed in kilometers per hour and the ratio of metatarsal-to-femur length. A least-squares regression on the data he collected produces the equation ŷ = 37.67 + 33.18x %3D where x is metatarsal-to-femur ratio and ŷ is predicted maximal sprint speed in kilometers per hour. The standard error of the intercept is 5.69 and the standard error of the slope is 7.94. Construct an 80% confidence interval for the slope of the population regression line. Give your answers precise to at least two decimal places. Lower limit: Upper limit:
A real estate analyst has developed a multiple regression line, y = 60 + 0.068 x1 – 2.5 x2, to predict y = the market price of a home (in $1,000s), using two independent variables, x1 = the total number of square feet of living space, and x2 = the age of the house in years. With this regression model, the predicted price of a 10-year old home with 2,500 square feet of living area is __________. $205.00 $200,000.00 $205,000.00 $255,000.00
The accompanying data represent the weights of various domestic cars and their gas mileages in the city. The linear correlation coefficient between the weight of a car and its miles per gallon in the city is r= - 0.972. The least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable is y= - 0.0070x + 44.4405. Complete parts (a) and (b) below. Click the icon to view the data table. ..... (a) What proportion of the variability in miles per gallon is explained by the relation between weight of the car and miles per gallon? The proportion of the variability in miles per gallon explained by the relation between weight of the car and miles per gallon is %. (Round to one decimal place as needed.) (b) Interpret the coefficient of determination. % of the variance in is by the linear model. Data Table (Round to one decimal p Full data set gas mileage Miles per Weight (pounds), x Weight (pounds), x Miles per Gallon, y Car Car Gallon, y…
A biologist is interested in predicting the percentage increase in lung volume when inhaling (y) for a certain species of bird from the percentage of carbon dioxide in the atmosphere (x). Data collected from a random sample of 20 birds of this species were used to create the least-squares regression equation ŷ = 400-0.08x. Which of the following best describes the meaning of the slope of the least-squares regression line? (A) The percentage increase in lung volume when inhaling increases by 0.08 percent, on average, for every 1 percent increase in the carbon dioxide in the atmosphere. (B) The percentage of carbon dioxide in the atmosphere increases by 0.08 percent, on average, for every 1 percent increase in lung volume when inhaling. (C) The percentage increase in lung volume when inhaling decreases by 0.08 percent, on average, for every 1 percent increase in the carbon dioxide in the atmosphere. (D) The percentage of carbon dioxide in the atmosphere increases by 0.08 percent, on…
An advertising firm wishes to demonstrate to potential clients the effectiveness of the advertising campaigns it has conducted. The firm is presenting data from 12 recent campaigns, with the data indicating an increase in sales for an increase in the amount of money spent on advertising. In particular, the least-squares regression equation relating the two variables cost of advertising campaign (denoted by x and written in millions of dollars) and resulting percentage increase in sales (denoted by y) for the 12 campaigns is y = 6.18 +0.14x, and the standard error of the slope of this least-squares regression line is approximately 0.10. Using this information, test for a significant linear relationship between these two variables by doing a hypothesis test regarding the population slope B₁. (Assume that the variable y follows a normal distribution for each value of x and that the other regression assumptions are satisfied.) Use the 0.10 level of significance, and perform a two-tailed…
The weight (in pounds) and height (in inches) for a child were measured every few months over a two-year period. The results are displayed in the scatterplot. The equation ŷ = 17.4 + 0.5x is called the least-squares regression line because it is least able to make accurate predictions for the data. makes the strongest association between weight and height. minimizes the sum of the squared distances from the actual y-value to the predicted y-value. maximizes the sum of the squared distances from the actual y-value to the predicted y-value.
A pediatrician wants to determine the relationship that exists between achild’s height, x, and head circumference, y. She randomly selects 11 children from her practice, measures their heights and head circumferences, and conducts the least-squares regression analysis with the simple linear model using StatCrunch. The output is given below: (a) Write down the equation of the least-squares regression line treating height as the explanatory variable and head circumference as the response variable. (b) Interpret the slope and y-intercept, if appropriate. (c) Use the regression equation to predict the head circumference of a child who is 25 inches tall. Assume that the regression model is applicable.(d) It is observed that one child who is 25 inches tall has a head circumference of 17.5 inches. Is the observed value above or below average among all children with heights of 25 inches?
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 = 83.5+ 2.21x₁ + 1.80x₂. The computer solution, based on a sample of eight weeks, provided SST = 25.4 and SSR = 23.495. (a) Compute and interpret R² and R2. (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 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 R2 = 0.595. Do you prefer the multiple regression results? Explain. Multiple regression analysis ---Select--- preferred since both R² and R2 show ---Select--- ✓percentage of the variability of y explained when both independent variables are used. . Adjusting for the number of…

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