Consider the “height-for-age” data below: Table 3: Height for age data Age in Years 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 Height in cm 102 107 112 116 121 126 130 136 143 149 154 158 161 162 163 a) Make a scatter plot of the data. [1] b) Find the least square regression line and add it to the scatter plot in Question 6 a). [3] c) Find the coefficient of determination and state what it tells us about the relationship between age and height.
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
Consider the “height-for-age” data below:
Table 3: Height for age data
Age in Years 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Height in cm 102 107 112 116 121 126 130 136 143 149 154 158 161 162 163
a) Make a
[1]
b) Find the least square regression line and add it to the scatter plot in Question 6 a).
[3]
c) Find the coefficient of determination and state what it tells us about the relationship between age and height.
d) Going by the relationship between Age and Height that you have established:
i) What would the
ii) Will the linear models be the best model for "height-for-age data"? JUSTIFY YOUR ANSWER
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