# (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)

### Principles of Instrumental Analysis

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

### 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+bWhen 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=∑xiyi−∑xi∑yiN and Sxx=∑xi2−(∑xi)2NSimilarly, 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

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