An elementary school teacher wants to see if there is a linear correlation between the ages of the elementary school students and their heights. The teacher randomly selects students from her elementary school and recorded the students' ages and heights below. Ages (in years) (x); 10 5 8 7 6 6 8 5 9 10 Height (in centimeters) (y): 127 102 119 111 96 100 114 87 123 120 (a) Find the correlation r between the ages and heights of the elementary school students. Use formula r=n(∑xy)−(∑x)(∑y)n(∑x2)−(∑x)2√⋅n(∑y2)−(∑y)2√r=n(∑xy)−(∑x)(∑y)n(∑x2)−(∑x)2⋅n(∑y2)−(∑y)2 Where ∑xy=8339,∑x=74,∑y=1099,∑x2=580,∑y2=122325∑xy=8339,∑x=74,∑y=1099,∑x2=580,∑y2=122325 (b) Find critical value for r. (c) Determine if there is significant linear correlation in the population using 0.05 significance level. (d) Clearly state the conclusion.
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.
An elementary school teacher wants to see if there is a
Ages (in years) (x); 10 5 8 7 6 6 8 5 9 10
Height (in centimeters) (y): 127 102 119 111 96 100 114 87 123 120
(a) Find the correlation r between the ages and heights of the elementary school students.
Use formula r=n(∑xy)−(∑x)(∑y)n(∑x2)−(∑x)2√⋅n(∑y2)−(∑y)2√r=n(∑xy)−(∑x)(∑y)n(∑x2)−(∑x)2⋅n(∑y2)−(∑y)2
Where ∑xy=8339,∑x=74,∑y=1099,∑x2=580,∑y2=122325∑xy=8339,∑x=74,∑y=1099,∑x2=580,∑y2=122325
(b) Find critical value for r.
(c) Determine if there is significant linear correlation in the population using 0.05 significance level.
(d) Clearly state the conclusion.
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