Use the following data to determine which factor is most predictive of test scores. For each independent variable, create a scatterplot for its relationship with test scores. Also calculate Pearson’s r for each variable. Based on the scatterplot and Pearson’s r, which factor has the strongest relationship with test scores? Student ID Test Score Sleep Hrs. Studied IQ GPA 1 67 6.5 4 90 2.9 2 77 8.5 7 102 2.8 3 96 7.5 16 130 3.8 4 61 4 5 93 2.2 5 89 9 11 125 3.1 6 73 6 5 106 2.4 7 93 8 17 122 3.4 8 58 5.5 2 88 1.7 9 75 8 6 100 2.4 10 82 10 8 107 3.0 11 90 12 14 118 3.6 12 69 11 3 92 2.0 13 84 7.5 9 103 3.2 14 78 6.5 13 77 2.8 15 63 2 2 99 2.5 16 87 9 8 114 3.3 17 76 8 8 110 2.4 18 70 11.5 1 125 2.8 19 72 10 4 86 2.1 20 50 3 0 70 1.5
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.
Use the following data to determine which factor is most predictive of test scores. For each independent variable, create a
Student ID Test Score Sleep Hrs. Studied IQ GPA
1 67 6.5 4 90 2.9
2 77 8.5 7 102 2.8
3 96 7.5 16 130 3.8
4 61 4 5 93 2.2
5 89 9 11 125 3.1
6 73 6 5 106 2.4
7 93 8 17 122 3.4
8 58 5.5 2 88 1.7
9 75 8 6 100 2.4
10 82 10 8 107 3.0
11 90 12 14 118 3.6
12 69 11 3 92 2.0
13 84 7.5 9 103 3.2
14 78 6.5 13 77 2.8
15 63 2 2 99 2.5
16 87 9 8 114 3.3
17 76 8 8 110 2.4
18 70 11.5 1 125 2.8
19 72 10 4 86 2.1
20 50 3 0 70 1.5
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