(a) Interpretation: The least-squares estimates of the slope and intercept for the given data set should be calculated. Concept introduction: The least-squares estimates of a set of data behaving linearly are defined as follows: y = m x + b When y and x are variables, m is the slope of the line and b is the y intercept . m can be calculated using: m = S x y S x x where, S x y = ∑ x i y i − ∑ x i ∑ y i N and S x x = ∑ x i 2 − ( ∑ x i ) 2 N Similarly, b can be calculated using: b = y ¯ − m x ¯ where, y ¯ = ∑ y i N and x ¯ = ∑ x i N ( x i and y i are individual pairs of data for x and y and N is the number of data pairs)

BuyFind

Principles of Instrumental Analysis

7th Edition
Douglas A. Skoog + 2 others
Publisher: Cengage Learning
ISBN: 9781305577213
BuyFind

Principles of Instrumental Analysis

7th Edition
Douglas A. Skoog + 2 others
Publisher: Cengage Learning
ISBN: 9781305577213

Solutions

Chapter 1, Problem 1.10QAP
Interpretation Introduction

(a)

Interpretation:

The least-squares estimates of the slope and intercept for the given data set should be calculated.

Concept introduction:

The least-squares estimates of a set of data behaving linearly are defined as follows:

y=mx+b

When y and x are variables, m is the slope of the line and b is the y intercept.

m can be calculated using:

m=SxySxxwhere,Sxy=xiyixiyiN and Sxx=xi2(xi)2N

Similarly, b can be calculated using:b=y¯mx¯where, y¯=yiN and  x¯=xiN(xi and yi are individual pairs of data for x and y and N is the number of data pairs)

Interpretation Introduction

(b)

Interpretation:

Standard deviations of the slope and intercept and the standard error of the estimates for the given data set should be calculated using the LINEST function in EXCEL.

Concept introduction:

In order to use the LINEST function in EXCEL to obtain statistical values for a given data set, the following command should be typed on an EXCEL spread sheet, in which the given data is already been typed in two columns.

=(known_ys,[known_xs],[constant],[stats])

Interpretation Introduction

(c)

Interpretation:

The 95% confidence intervals for the slope and the intercept should be determined.

Concept introduction:

The general formula to calculate the 95% confidence intervals for a statistic relevant to a regression analysis is as follows:

95% CI for a given statistic=staistic value± critical value for the confidence interval×standard error of the statisticFor slope (m), the equation can be rewritten as,95% CI=m±t×SmFor intercept (b), the equation can be rewritten as,95% CI=b±t×Sb

Interpretation Introduction

(d)

Interpretation:

The glucose concentration and its standard deviation of a serum sample, which gave an absorbance of 0.350 should be calculated.

Concept introduction:

To determine an unknown glucose concentration c from the least-squares line, the valueof the absorbancey, the slope ( m ) and intercept ( b ) can be used as follows,

cx=ycbm

The standard deviation of c ( Sc ) is calculated by,

Sc=Sym1M+1N+(y¯cy¯)2m2SxxWhere,M=number of replicate resultsN=number of standardsy¯c=mean response for the unknownSy,y¯, and Sxx were defined in early steps.

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