A researcher collected data on ( X, Y ), and wanted to test if the true relationship is linear.Therefore, she collected replicated values of X. Here is a summary of the data, and some results:Xi No. of replicates yiSSE = 312.139105118.32121444.151339665111071848375At significance level a = 0.05, carry out the test of Lack-of-Fit for linearity of the model.No need to show an ANOVA Table.Calculations:Test statistic: T =Critical value =Conclusion: Sincewe2.

To test whether true relationship is linear or not, consider Lack of fit F-test. H0: There is no…

Answered: A researcher collected data on ( X , Y…

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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Here is a bivariate data set. Find the regression equation for the response variable y. x y 60.9 36.2 55.8 44.3 27.8 61.7 36.1 56.3 56 53.7 49.8 55.2 45.7 51.5 60.1 46.6 63.1 50 63.9 40.2 68.8 45.4 32.3 60.4 76.6 40.6 65.4 46 65.6 42.7 regression equation: Enter the equation in slope-intercept form with parameters accurate to three decimal places.
A trucking company considered a multiple regression model for relating the dependent variable of total daily travel time for one of its drivers (hours) to the predictors distance traveled (miles) and the number of deliveries of made. After taking a random sample, a multiple regression was performed and the output is given below. Interpret the slope of the deliveries variable. When deliveries increases by 0.805 units, time increases by 1 hour, holding all other variables constant. 2) We do not have enough information to say. 3) When deliveries increases by 1 unit, time decreases by 0.805 hours, holding all other variables constant. 4) When deliveries decreases by 1 unit, time increases by 0.805 hours, holding all other variables constant. 5) When deliveries increases by 1 unit, time increases by 0.805 hours, holding all other variables constant.
One set of 20 pairs of scores, X and Y values, produces a correlation of r = 0.70. If SSY = 150, calculate the standard error of the estimate for the regression line
A paper suggests that the simple linear regression model is reasonable for describing the relationship between y = eggshell thickness (in micrometers, µm) and x = egg length (mm) for quail eggs. Suppose that the population regression line is y = 0.125 + 0.007x and that ?e = 0.005. Then, for a fixed x value, y has a normal distribution with mean 0.125 + 0.007x and standard deviation 0.005. (a) What is the mean eggshell thickness for quail eggs that are 15 mm in length? ____ µm What is the mean eggshell thickness for quail eggs that are 17 mm in length? ____ µm (b) What is the probability that a quail egg with a length of 15 mm will have a shell thickness that is greater than 0.23 µm? _____ (c) Approximately what proportion of quail eggs of length 14 mm have a shell thickness of greater than 0.222? (Hint: The distribution of y at a fixed x is approximately normal. Round your answer to four decimal places.) ____ Approximately what proportion of quail eggs of length…
On the second sheet is data which shows the rate of growth of a particular patch of bamboo vs daily high temperature.(a) Construct a scatterplot, including the equation of the line of best fit and value of R2.(b) What would the predicted growth rate be for a day with a temperature of 84◦?(c) Is there evidence, at α = 0.01, to support a claim that there is a linear relationship between temperature and growth rate? Please state clearly the null hypothesis, the alternative hypothesis, and what decision you make.
A student working on a physics project investigated the relationship between the speed and the height of roller coasters. The student collected data on the maximum speed, in miles per hour, and the maximum height, in feet, for a random sample of 2121 roller coasters, with the intent of testing the slope of the linear relationship between maximum speed and maximum height. However, based on the residual plot shown, the conditions for such a test might not be met.
A random sample of non-industrialized countries was selected and the life expectancy in years is listed for both men and women. Given that the correlation coefficient is significant. Find the equation of the regression line men,x :59.7, 72.9,41.9,46.2,50.3,43.2 Women,y :63.8,77.8,44.5,48.3,54.0,43.5
Consider a linear spline with 16 knots. How many regression coefficients do you estimate when running a linear regression model with that spline?
After performing a statistical regression on a set of data the value of the correlation coefficient r was -0.2041. What does that imply about the data?
Suppose that a regional express delivery service company wants to estimate the cost of shipping a package (Y) as a function of cargo type, where cargo type includes the following possibilities: fragile, semi-fragile, and durable. Costs for 15 randomly chosen packages of approximately the same weight and same distance shipped, but of different cargo types, are provided in the file P14_16.xlsx. a. Estimate a regression equation using the given sample data, and interpret the estimated regression coefficients. b. According to the estimated regression equation, which cargo type is the most costly to ship? Which cargo type is the least costly to ship? c. How well does the estimated equation fit the given sample data? How might the fit be improved? d. Given the estimated regression equation, predict the cost of shipping a package with semi-fragile cargo.
A study was done to determine the relationship between the alcohol content of beer, and the amount of calories in a 12 oz serving size. The sample data is provided in the data below. a) From this sample data, can you conclude (at the alpha=0.05 level) that there is in fact a linear correlation between the two variables? Use the statistics (correlation coefficient, value) to describe the correlation (if any). B) Using the sample data, find a regression equation to estimate the number of calories in a beer. C) Dogfish Head Brewery in Milton, Delaware has an I.P.A. beer called "120 minute IPA" which has an alcohol content of 18%. Using your regression equation, estimate the number of calories in a 12 oz serving of 120 Minute. Brand/Beer Alcohol Content (%) Calories (per 12 oz) Big Sky Scape Goat Pale Ale 4.70 163 Sierra Nevada Harvest Ale 6.70 215 Steel Reserve 8.10 222 Coors Light 4.15 104 Genesee Cream Ale 5.10 162 Sierra Nevada Summeefest Beer 5.00 158 Michelob Beer…
A zoologist selected 12 black bears in a Canadian habitat at random to examine the relationship between the age in years, xx, and the weight in tens of pounds, yy. The 95 percent confidence interval for estimating the population slope of the linear regression line predicting weight in tens of pounds based on the age in years is given by 1.272±0.5701.272±0.570. Assume that the conditions for inference for the slope of the regression equation are met. Which of the following is the correct interpretation of the interval? A)We are 95 percent confident that the mean increase in the weight of a black bear for each one-year increase in the age of the bear is between 7.0 and 18.4 pounds. B)We are 95 percent confident that an increase of one year in the age of an individual black bear will result in an increase in the black bear’s weight of between 7.0 and 18.4 pounds. C)We are 95 percent confident that for every one-year increase in the age of black bears in the sample,…

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A researcher collected data on ( X , Y ), and wanted to test if the true relationship is linear. Therefore, she collected replicated values of X. Here is a summary of the data, and some results: Xi No. of replicates y; SSE = 312. 1 3 9 10 2 5 11 8 3 12 14 4 4 15 13 5 3 9 6 11 10 7 8. 4 8 3 7 CO 2.