Consider the following table of data.x 0 1 2y 4 1 0 1341 4(a) Calculate the least squares line and the correlationcoefficient.(b) Sketch a graph of the data.(c) Comparing your answers to parts (a) and (b), does a cor-relation coefficient of 0 mean that there is no relationshipbetween the x- and y- values? Would some curve otherthan a line fit the data better? Explain.

x y xy x^2 X = x-x̄ Y= y - ȳ XY 0 4 0 0 -2 2 -4 1 1 1 1 -1 -1 1 2 0 0 4 0 -2 0 3 1 3 9 1 -1…

Answered: Consider the following table of data. x…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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An engineer wants to determine how the weight of a gas-powered car, x, affects gas mileage, y. The accompanying data represent the weights of various domestic cars and their miles per gallon in the city for the most recent model year. Complete parts (a) through (d) below. LOADING... Click here to view the weight and gas mileage data. Question content area bottom Part 1 (a) Find the least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable. ModifyingAbove y with caretyequals=enter your response herexplus+(enter your response here) (Round the x coefficient to five decimal places as needed. Round the constant to one decimal place as needed.)
(b) For the (x, y) data set of part (a), compute the equation of the sample least-squares line ŷ = a + bx. (Use 4 decimal places.) a b If the per capita spending was x = $39 one year, what do you predict for the spending the next year? (Use 2 decimal places.) $ per capita (c) Compute the sample correlation coefficient r and the coefficient of determination r2. (Use 4 decimal places.) r r2 Test ρ > 0 at the 1% level of significance. (Use 2 decimal places.) t critical t
(a) The correlation coefficient: r = (b) The least squares line: ỹ = %3D
1.)fill in the blanks. Based on the physician's study, the predictor variable, X is_____and the response variable, Y, is________. 2.) As described in the article, the relation between age and peak heart is a______. - positive relation - negative relation - no relation 3.) Provide the regression line, ŷ=a+bx. Show steps/equations used to get answer. 4.) Suppose a 40 year old person is randomely selected. Use your Model to predict their peak heart rate. 5.) Based on your model, as a person ages one year, how much would you expect peak heart rate to change?
The least-squares regression equation is y=784.6x+12,431 where y is the median income and x is the percentage of 25 years and older with at least a bachelor's degree in the region. The scatter diagram indicates a linear relation between the two variables with a correlation coefficient of 0.7962. In a particular region, 26.5 percent of adults 25 years and older have at least a bachelor's degree. The median income in this region is $29,889. Is this income higher or lower than what you would expect? Why?
The basic hypothesis is that people who play sports are more likely than others to watch sport on TV. Your first task is to crosstabulate the data involving the playing and watching of sports and to determine the direction and strength of that relationship. Write out your findings about this basic relationship. Your next task is to determine the direction and strength of the partial relationships when you control for the gender of individuals.
The following table shows students’ number of absences, x, and the student’s final grade,, y.# of absences x 6 2 15 9 12 5 8 Final grade y 82 86 43 74 58 90 78a) Calculate r, the correlation coefficient ________________b) Find the equation of the regression line __________________________________c) If a student is absent 4 times,, what grade does your regression line predict?__________________
Part C

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