Question

The following table shows the scores in an intelligence test of 65 students of different age groups.Find the correlation coefficient between age and scores of the test.Also find coefficient of determination.

scores
Age in years
Total


18
19
20
21


200-250
4
4
2
1
11

250-300
3
5
4
2
14

300-350
2
6
8
5
21

350-400
1
4
6
10
21

Total
10
19
20
18
67
​

Answer 1

Answer:

The present review introduces methods of analyzing the relationship between two quantitative variables. The calculation and interpretation of the sample product moment correlation coefficient and the linear regression equation are discussed and illustrated. Common misuses of the techniques are considered. Tests and confidence intervals for the population parameters are described, and failures of the underlying assumptions are highlighted.

Keywords: coefficient of determination, correlation coefficient, least squares regression line

Introduction

The most commonly used techniques for investigating the relationship between two quantitative variables are correlation and linear regression. Correlation quantifies the strength of the linear relationship between a pair of variables, whereas regression expresses the relationship in the form of an equation. For example, in patients attending an accident and emergency unit (A&E), we could use correlation and regression to determine whether there is a relationship between age and urea level, and whether the level of urea can be predicted for a given age.

Scatter diagram

When investigating a relationship between two variables, the first step is to show the data values graphically on a scatter diagram. Consider the data given in Table Table1.1. These are the ages (years) and the logarithmically transformed admission serum urea (natural logarithm [ln] urea) for 20 patients attending an A&E. The reason for transforming the urea levels was to obtain a more Normal distribution [1]. The scatter diagram for ln urea and age (Fig. (Fig.1)1) suggests there is a positive linear relationship between these variables.