Answered: A paper suggests that the simple linear… | bartleby

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter4: Equations Of Linear Functions

Section4.6: Regression And Median-fit Lines

Problem 4GP

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A paper suggests that the simple linear regression model is reasonable for describing the relationship between y = eggshell
thickness (in micrometers, Pm) and x = egg length (mm) for quail eggs. Suppose that the population regression line is
y = 0.115 + 0.005x and that o = 0.005. Then, for a fixed x value, y has a normal distribution with mean 0.115 + 0.005x and
standard deviation 0.005.

(c) Approximately what proportion of quail eggs of length 14 mm have a shell thickness of greater than 0.182? (Hint: The
distribution of y at a fixed x is approximately normal. Round your answer to four decimal places.)
1
Approximately what proportion of quail eggs of length 14 mm have a shell thickness of less than 0.187? (Round your
answer to four decimal places.)
1

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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…
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 = 0.185 + 0.007x and that ?e = 0.005. Then, for a fixed x value, y has a normal distribution with mean 0.185 + 0.007x and standard deviation 0.005. (You may need to use a table.) b)What is the probability that a quail egg with a length of 15 mm will have a shell thickness that is greater than 0.29 µm? (c)Approximately what proportion of quail eggs of length 14 mm have a shell thickness of greater than 0.281? (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 14 mm have a shell thickness of less than 0.286? (Round your answer to four decimal places.)
Consider a linear regression model for the decrease in blood pressure (mmHg) over a four-week period with muy=2.8+0.8x and standard deviation chi=3.2. The explanatory variable x is the number of servings fruits and vegetables in a calorie-controlled diet. The decrease in blood pressure y will vary about this subpopulation mean. What is the distribution of y for this subpopulation?
If the R-squared for a regression model relating the outcome y to an explanatory variable x is 0.9. This implies that y and x are positively correlated.
If the error term in a linear regression model is normally distributed, then the distribution of the OLS estimator, conditional on explanatory variables, is also normal. True or False, why?
If the standard error of the estimate for a regression model fitted to a large number of paired observations is 1.75, approximately 95% of the residuals would lie within ______. −3.50 and +3.50 −1.75 and +1.75 −0.95 and +0.95 −0.68 and +0.68 −0.97 and +0.97
For variables x1, x2, x3, and y satisfying the assumptions for multiple linear regression inferences, the population regression equation is y = 27 – 4.7x1 + 2.3x2 + 5.8x3. For samples of size 20 and given values of the predictor variables, the distribution of the estimates of ß1 for all possible sample regression planes is a _________ distribution with mean a_________ and standard deviation _______.
Using the regression line attached. Based on only the above plot, one can conclude: a) height causes an increase in weight b) weight causes an increase in height c) taller people are more likely to weigh more than shorter people, at least in the sample on which this data is based d) a statistically significant predictive relationship between height and weight e) c and d

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