(a) Interpretation: Fit a line to given data using the method of least squares. Concept introduction: The method of least square for a y = ax + b line is given as, here, a and b can be calculated as, S x y = 1 n ∑ i = 1 n X i Y i S x x = 1 n ∑ i = 1 n X i 2 S x = 1 n ∑ i = 1 n X i h e n c e , a = S x y − S x S y S x x − ( S x ) 2 b = S x x S y − S x S x y S x x − ( S x ) 2

Question

Want to see the full answer?

Answer 1

Question

Chapter 2, Problem 2.48P

Interpretation Introduction

(a)

Interpretation:

Fit a line to given data using the method of least squares.

Concept introduction:

The method of least square for a y = ax + b line is given as, here, a and b can be calculated as,

Sxy = 1n ∑i=1nXiYiSxx =1n∑i=1nXi2Sx = 1n∑i=1nXi

hence,a = Sxy−Sx Sy Sxx − (Sx )2b = SxxSy−Sx Sxy Sxx − (Sx )2

Interpretation Introduction

(b)

Interpretation:

Fit a line through the origin using the same data set.

Concept introduction:

The method of least square for a y = ax + b line is given as, here, a and b can be calculated as,

Sxy = 1n ∑i=1nXiYiSxx =1n∑i=1nXi2Sx = 1n∑i=1nXi

hence,a = Sxy−Sx Sy Sxx − (Sx )2b = SxxSy−Sx Sxy Sxx − (Sx )2

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Students have asked these similar questions

Use the References to access important values if needed for this question. You have the following data points which belong to a function of the form y = ae", where b can be positive or negative. 4.13 3.26 2.57 0.100 0.200 0.300 You wish to determine the value of the constant, 6, and to do so you will construct a linear plot. What will you plot against what? y-axis label: Iny - x-axis label: x From the values of a and y in the table above, calculate the values of the three corresponding data points. Click on the graph below, and use the "Freeform Curves" tool to plot the data. Line segments will automatically connect the points. Enter Solution What is the numerical value of the constant, b? b = Submit Answer Retry Entire Group No more group attempts remain

Find the mean and median of each of the following sets of data. Determine the deviation from the mean for each data point within the seats and find the mean deviation for each set. Use a spreadsheet if it is convenient. (a) 0.0110 0.0104. 0.0105

The following linear plot is derived from a function of the form Y = ae", where a and b are constants. 7 6 5 4 2 1 0 0.1 0.2 0.3 0.4 0.5 0.6 For the function y = ae' bx from which the data points on the graph were derived, the numerical value of the constants are a = and b = In y

Answer 2

Question

Chapter 2, Problem 2.48P

Interpretation Introduction

(a)

Interpretation:

Fit a line to given data using the method of least squares.

Concept introduction:

The method of least square for a y = ax + b line is given as, here, a and b can be calculated as,

Sxy = 1n ∑i=1nXiYiSxx =1n∑i=1nXi2Sx = 1n∑i=1nXi

hence,a = Sxy−Sx Sy Sxx − (Sx )2b = SxxSy−Sx Sxy Sxx − (Sx )2

Interpretation Introduction

(b)

Interpretation:

Fit a line through the origin using the same data set.

Concept introduction:

The method of least square for a y = ax + b line is given as, here, a and b can be calculated as,

Sxy = 1n ∑i=1nXiYiSxx =1n∑i=1nXi2Sx = 1n∑i=1nXi

hence,a = Sxy−Sx Sy Sxx − (Sx )2b = SxxSy−Sx Sxy Sxx − (Sx )2

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 3

Question

Chapter 2, Problem 2.48P

Interpretation Introduction

(a)

Interpretation:

Fit a line to given data using the method of least squares.

Concept introduction:

The method of least square for a y = ax + b line is given as, here, a and b can be calculated as,

Sxy = 1n ∑i=1nXiYiSxx =1n∑i=1nXi2Sx = 1n∑i=1nXi

hence,a = Sxy−Sx Sy Sxx − (Sx )2b = SxxSy−Sx Sxy Sxx − (Sx )2

Interpretation Introduction

(b)

Interpretation:

Fit a line through the origin using the same data set.

Concept introduction:

The method of least square for a y = ax + b line is given as, here, a and b can be calculated as,

Sxy = 1n ∑i=1nXiYiSxx =1n∑i=1nXi2Sx = 1n∑i=1nXi

hence,a = Sxy−Sx Sy Sxx − (Sx )2b = SxxSy−Sx Sxy Sxx − (Sx )2

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 4

Question

Chapter 2, Problem 2.48P

Interpretation Introduction

(a)

Interpretation:

Fit a line to given data using the method of least squares.

Concept introduction:

The method of least square for a y = ax + b line is given as, here, a and b can be calculated as,

Sxy = 1n ∑i=1nXiYiSxx =1n∑i=1nXi2Sx = 1n∑i=1nXi

hence,a = Sxy−Sx Sy Sxx − (Sx )2b = SxxSy−Sx Sxy Sxx − (Sx )2

Interpretation Introduction

(b)

Interpretation:

Fit a line through the origin using the same data set.

Concept introduction:

The method of least square for a y = ax + b line is given as, here, a and b can be calculated as,

Sxy = 1n ∑i=1nXiYiSxx =1n∑i=1nXi2Sx = 1n∑i=1nXi

hence,a = Sxy−Sx Sy Sxx − (Sx )2b = SxxSy−Sx Sxy Sxx − (Sx )2

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 5

Chapter 2, Problem 2.48P

Interpretation Introduction

(a)

Interpretation:

Fit a line to given data using the method of least squares.

Concept introduction:

The method of least square for a y = ax + b line is given as, here, a and b can be calculated as,

Sxy = 1n ∑i=1nXiYiSxx =1n∑i=1nXi2Sx = 1n∑i=1nXi

hence,a = Sxy−Sx Sy Sxx − (Sx )2b = SxxSy−Sx Sxy Sxx − (Sx )2

Interpretation Introduction

(b)

Interpretation:

Fit a line through the origin using the same data set.

Concept introduction:

The method of least square for a y = ax + b line is given as, here, a and b can be calculated as,

Sxy = 1n ∑i=1nXiYiSxx =1n∑i=1nXi2Sx = 1n∑i=1nXi

hence,a = Sxy−Sx Sy Sxx − (Sx )2b = SxxSy−Sx Sxy Sxx − (Sx )2

Answer 6

Chapter 2, Problem 2.48P

Interpretation Introduction

(a)

Interpretation:

Fit a line to given data using the method of least squares.

Concept introduction:

The method of least square for a y = ax + b line is given as, here, a and b can be calculated as,

Sxy = 1n ∑i=1nXiYiSxx =1n∑i=1nXi2Sx = 1n∑i=1nXi

hence,a = Sxy−Sx Sy Sxx − (Sx )2b = SxxSy−Sx Sxy Sxx − (Sx )2

Answer 7

Chapter 2, Problem 2.48P

Interpretation Introduction

(a)

Interpretation:

Fit a line to given data using the method of least squares.

Concept introduction:

The method of least square for a y = ax + b line is given as, here, a and b can be calculated as,

Sxy = 1n ∑i=1nXiYiSxx =1n∑i=1nXi2Sx = 1n∑i=1nXi

hence,a = Sxy−Sx Sy Sxx − (Sx )2b = SxxSy−Sx Sxy Sxx − (Sx )2

Answer 8

Interpretation Introduction

(b)

Interpretation:

Fit a line through the origin using the same data set.

Concept introduction:

The method of least square for a y = ax + b line is given as, here, a and b can be calculated as,

Sxy = 1n ∑i=1nXiYiSxx =1n∑i=1nXi2Sx = 1n∑i=1nXi

hence,a = Sxy−Sx Sy Sxx − (Sx )2b = SxxSy−Sx Sxy Sxx − (Sx )2

Answer 9

Interpretation Introduction

(b)

Interpretation:

Fit a line through the origin using the same data set.

Concept introduction:

The method of least square for a y = ax + b line is given as, here, a and b can be calculated as,

Sxy = 1n ∑i=1nXiYiSxx =1n∑i=1nXi2Sx = 1n∑i=1nXi

hence,a = Sxy−Sx Sy Sxx − (Sx )2b = SxxSy−Sx Sxy Sxx − (Sx )2

Answer 10

Expert Solution & Answer

Answer 11

Expert Solution & Answer

Answer 12

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 13

Ch. 2 - Prob. 2.1P Ch. 2 - Prob. 2.2P Ch. 2 - Prob. 2.3P Ch. 2 - Prob. 2.4P Ch. 2 - Prob. 2.5P Ch. 2 - Prob. 2.6P Ch. 2 - Prob. 2.7P Ch. 2 - Prob. 2.8P Ch. 2 - Prob. 2.9P Ch. 2 - Prob. 2.10P

Solution Summary: The author explains how the method of least squares is used to fit a line to given data.

Concept explainers

Want to see the full answer?

Chapter 2 Solutions