The accompanying table shows the ages (in years) of 11 children and the numbers of words in their vocabulary. Complete parts (a) through (d) below. Age, x Vocabulary size, y 1 5 2 240 3 560 4 1200 5 1900 6 2600 3 540 5 2200 2 280 4 1300 6 2300 (a) Display the data in a scatter plot. (b) Calculate the sample correlation coefficient r. (c) Describe the type of correlation, if any, and interpret the correlation in the context of the data. (d) Use the table of critical values for the Pearson correlation coefficient to make a conclusion about the correlation coefficient. Let α=0.01.
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.
The accompanying table shows the ages (in years) of 11 children and the numbers of words in their vocabulary. Complete parts (a) through (d) below.
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