11.21 Consider the following pairs of measurements.DL11021xy5454333-1273018655433a. Construct a scatterplot of these data.b. What does the scatterplot suggest about the relation-ship between x and y?xxc. Given that SS = 43.4286, SSxy = 39.8571, y = 3.4286,and 3.7143, calculate the least squares estimates ofBo and B. 020; .918d. Plot the least squares line on your scatterplot. Does theline appear to fit the data well? Explain.e. Interpret the y-intercept and slope of the least squaresline. Over what range of x are these interpretationsmeaningful?

Step 1: List the given values.We are given the following data set: XY5433-1021786543Step 2: Discuss…

Answered: 11.21 Consider the following pairs of…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.3: Least Squares Approximation

Problem 29EQ

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Please do the last three parts only
A data set is given below. (a) Draw a scatter diagram. Comment on the type of relation that appears to exist between x and y. (b) Given that x=3.8333, sx=2.4014, y=3.6500, sy=1.7942, and r=−0.9539, determine the least-squares regression line. (c) Graph the least-squares regression line on the scatter diagram drawn in part (a).
A data set is given below. (a) Draw a scatter diagram. Comment on the type of relation that appears to exist between x and y. (b) Given that x = 3.8333, sy = 2.4014, y = 4.0500, sy = 1.5997, and r= - 0.9345, determine the least-squares regression line. (c) Graph the least-squares regression line on the scatter diagram drawn in part (a). 2 4 6. y 5.8 5.8 4.7 3.2 2.2 2.6 (a) Choose the correct graph below. O A. O B. C. Ay 6- Ay 6- Ay 6- 6- X X 0- 0- 0- 6. 6 6. There appears to be a linear, negative relationship. (b) y =x+ (O %3D (Round to three decimal places as needed.)
A data set is given below. (a) Draw a scatter diagram. Comment on the type of relation that appears to exist between x and y. (b) Given that x = 3.6667, sy =2.3381, y = 3.9167, s, = 1.8563, and r= - (c) Graph the least-squares regression line on the scatter diagram drawn in part (a). 0.9570, determine the least-squares regression line. 1 1 y 5.1 6.4 5.1 2.8 1.9 2.2 (a) Choose the correct graph below. O A. В. Ay 7- Ay 7- Ay 7- X X 6 6 6. There appears to be a linear, negative relationship. (b) y =x+ (O (Round to three decimal places as needed.)
L11046 X y 11.46 Consider the following pairs of observations: 1 1 4 3 3 3 2 1 5 4 6 7 0 2 a. Construct a scatterplot for the data. b. Use the method of least squares to fit a straight line to the seven data points in the table. c. Plot the least squares line on your scatterplot of part a. d. Specify the null and alternative hypotheses you would use to test whether the data provide sufficient evidence to indicate that x contributes information for the (linear) prediction of y. e. What is the test statistic that should be used in conducting the hypothesis test of part d? Specify the degrees of freedom associated with the test statistic. f. Conduct the hypothesis test of part d using a = = .05.
11.13 please do it in steps because i don't know
Q.3. Table shows the age in years and the retail value in thousands of dollars of a random sample of ten automobiles of the same make and model. a) Compute the linear correlation| coefficient. Interpret its value in the context of the problem. b) Compute the least squares regression line Data on Age and Value of Used Automobiles of a Specific Make and Model 2 3 3 3 4 4 5 5 28.7 24.8 26.0 30.5 23.8 24.6 23.8 20.4 21.6 22.1
A simple linear regression was performed on 25 observations. The least squares calculations are given as: SSxy = 204, SSxx= 100, SSyy = 516. Calculate SSE. O 99.84 O 4.34 O 516 O 2.04
12.21 In the study of Exercise 12.9, 25 observations were used to calculate the least squares estimates. The regression sum of squares and error sum of squares were found to be as follows: SSR 79.2 and SSE = 45.9 = a. Find and interpret the coefficient of determination. b. Find the adjusted coefficient of determination. c. Find and interpret the coefficient of multiple correlation.
Suppose a doctor measures the height, x, and head circumference, y, of 8 children and obtains the data below. Thecorrelation coefficient is 0.944 and the least squares regression line is y = 0.199x + 11.982. Complete parts (a) and (b)below.Height, x27.5 25.5 26.25 25.25 27.5 26.25 26 27.25 27.25 27 27.25 ФHead Circumference, # 17.5 17.0 17.2 17.0 17.5 17.3 17.2 17.4 17.3 17.3 17.4(a) Compute the coefficient of determination, R?R?.% (Round to one decimal place as needed.)(b) Interpret the coefficient of determination and comment on the adequacy of the linear model.Approximately % of the variation inis explained by the least-squares regression model.According to the residual plot, the linear model appears to be (Round to one decimal place as needed.)
c. Which of the following is the correct graph of the given data? -ОА. 10 1012 12 10 O C. 12- 81012 1012 Using the graph, explain the dramatic difference between the answers to parts (a) and (b). Choose the correct answer below. OA. The point (10,10) is not an outier, but it does have a strong effect on the least squares line and the correlation coefficient. OB. The point (10,10) does not have any effect on the least squares line and the correlation coefficient. OC. The point (10,10) is an outler that has a weak effect on the least squares line and the correlation coefficient. OD. The point (10,10) is an outlier that has a strong effect on the least squares line and the correlation coefficient.
Given are five observations for two variables, and y. The estimated regression equation for these data is = 75.74-2.92x. a. Compute SSE, SST, and SSR. Yi The least squares line provided an - Select your answer decimal). fit; 4 SSE (to 2 decimals) SST (to 2 decimals) SSR (to 2 decimals) b. Compute the coefficient of determination ². Comment on the goodness of fit. (to 3 decimals) 00 15 18 20 57 57 46 17 12 Check My Work (2 remaining) % of the variability in y has been explained by the estimated regression equation (to 1 c. Compute the sample correlation coefficient. Enter negative value as negative number. (to 3 decimals)

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