Use the method of least squares to obtain a straight line which best fits these data points.a) Fill out the table belowI7yxyIΣr² =Σry =Σε ΞΣy =b) Use the provided formulas to find a formula for the regression line (also called the line of bestfit).Ν(Σxy) - (Στ) (ΣΜ)A =N (Cr²)-(C1)²2B =(Σy) - Α(Σ)N

Step 1: Defining the problem.The least squares method is the process of finding a regression line…

Answered: Use the method of least squares to…

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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Given are five observations for two variables, x and y. xi 3 12 6 20 14 yi 55 45 50 15 20 #1) Develop the estimated regression equation by computing the values of b0 and b1 using b1 = Σ(xi − x)(yi − y) Σ(xi − x)2 and b0 = y − b1x. y= #2) Use the estimated regression equation to predict the value of y when x = 13.
Factor and simplify algebraic expression. x3/2 - x1/2
Consider the data, X, 1 4 Y, 4 8 6 10 12 The estimated regression equation for these data is ý- 2.60 + 1.80x. (a) Compute SSE, SST, and SSR using equations SSE - I(r, - ), sST - E(y, - v), and SSR = E(, - . SSE 7.6 SST =40 SSR = 324 (b) Compute the coefficient of determination ?. Comment on the goodness of fit. (For purposes of this exercise, consider a proportion large if it is at least 0.55.) O The least squares line did not provide a good fit as a large proportion of the variability in y has been explained by the least squares line. O The least squares line did not provide a good fit as a small proportion of the variability in y has been explained by the least squares line. O The least squares line provided a good fit as a small proportion of the variability in y has been explained by the least squares line The least squares line provided a good fit as a large proportion of the variability in y has been explained by the least squares ine. (c) Compute the sample correlation…
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7) The accompanying data show the number of bacteria present after a certain number of hours. Find the equation of the regression line for the data. Then construct a scatter plot of (x,y) and sketch the regression line with i Number of hours, x Number of bacteria, y1 1672 2783 4684 7835 13146 19277 4910 The equation of the regression line is y=x+ (Round to two decimal places as needed.) Construct a scatter plot of the data and draw the regression line. Choose the correct graph below.
Q#2: (a) Calculate the estimated multiple linear regression equation for the following data using the multiplication in deviation form ΣΥ- 89, ΣΧ30 ΣΧ52 ΣX 238, EX = 582 £X¡Y = 619, EX1X2 %3| %3D 351, EX2Y = 1007,n = 5 %3D
Use the table and the given regression equation to answer parts (a)-(e). 3 y=4-4x -8 X y SSE= No Yes 1 0 a. Compute the three sums of squares, SST, SSR, and SSE, using the defining formulas. SST = (Type an integer or a decimal.) SSR = (Type an integer or a decimal.) (Type an integer or a decimal.) b. Verify the regression identity, SST = SSR + SSE. Is this statement correct? 20 O A. Not useful -4 c. Determine the value of r2², the coefficient of determination. 2 (Round to four decimal places as needed.) d. Determine the percentage of variation in the observed values of the response variable that is explained by the regression. % (Round to two decimal places as needed.) e. State how useful the regression equation appears to be for making predictions.
It is required to use the data given in the table to estimate the parameters of the multiple linear regression equation by any of the estimation methods:
Use the following equations to find the least square regression quadratic for the given points. Use the regression capabilities of a graphing utility to verify your results. Σ +b + C |= 1 i = 1 in 3 + b' 2 + a |= 1 i = 1 i = 1 n n a + cn = X; i = 1 i = 1 i = 1 (0, 10), (1, 9), (2, 6), (3, 0) y =
Solve part c and d. Thank you.
Given are five observations for two variables, and y. a. Choose the correct scatter diagram for these data: A. C. D 60 50 40 30- 20 -10- 60 50 40 -30 20 10- 10 10 20 20 30 30 40 40 50 50 60 x 60 x B. D. 60 50 40 30 20 10- 60 50 40 30- 20 10- 10 10 20 20 30 30 40 40 50 50 60 x 60 x 5 15 8 23 19 Xi Yi 55 40 50 15 25 b. What does the scatter diagram developed in part (a) indicate about the relationship between the two variables? There appears to be a negative linear relationship between x and y. and y by drawing a straight line through the data. c. Try to approximate the relationship between Many different straight lines can be drawn ✔ to provide a linear approximation of the relationship between x and y.

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