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…

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 5PPS

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Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4
Respiratory Rate Researchers have found that the 95 th percentile the value at which 95% of the data are at or below for respiratory rates in breath per minute during the first 3 years of infancy are given by y=101.82411-0.0125995x+0.00013401x2 for awake infants and y=101.72858-0.0139928x+0.00017646x2 for sleeping infants, where x is the age in months. Source: Pediatrics. a. What is the domain for each function? b. For each respiratory rate, is the rate decreasing or increasing over the first 3 years of life? Hint: Is the graph of the quadratic in the exponent opening upward or downward? Where is the vertex? c. Verify your answer to part b using a graphing calculator. d. For a 1- year-old infant in the 95 th percentile, how much higher is the walking respiratory rate then the sleeping respiratory rate? e. f.
YOUR TURN 1 Calculate the least squares line for the following data. x 1 2 3 4 5 6 y 3 4 6 5 7 8
Cellular Phone Subscribers The table shows the numbers of cellular phone subscribers y in millions in the United States from 2008 through 2013. Source: CTIA- The Wireless Association Year200820092010201120122013Number,y270286296316326336 (a) Find the least squares regression line for the data. Let x represent the year, with x=8 corresponding to 2008. (b) Use the linear regression capabilities of a graphing utility to find a linear model for the data. How does this model compare with the model obtained in part a? (c) Use the linear model to create a table of estimated values for y. Compare the estimated values with the actual data.

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