1. Consider the following data of the number of hours 12 students spent online during the weekend and the scores of each student who took a test the following Monday. Hrs spent online(x) 0 1 2 3 3 5 5 5 6 7 7 10 Test scores(y) 96 85 82 74 95 68 76 84 58 65 75 50 a. Find the sample linear correlation coefficient and interpret it. b. Is the population correlation coefficient significant? [ use α= 0.05] c. Find the equation of the regression line. What is the slope of the line? Interpret this value in the context?
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.
1. Consider the following data of the number of hours 12 students spent online during the weekend and the scores of each student who took a test the following Monday.
Hrs spent
online(x)
0
1
2
3
3
5
5
5
6
7
7
10
Test scores(y)
96
85
82
74
95
68
76
84
58
65
75
50
a. Find the sample linear
b. Is the population correlation coefficient significant? [ use α= 0.05]
c. Find the equation of the regression line. What is the slope of the line? Interpret this value in the context?
d. What is the coefficient of determination? Interpret the result?
e. If ? were 3.5 hours, what would you expect ? to be?
f. If ? were 5 hours, what would you expect ? to be?
g. If ? were 20 hours, what would you expect ? to be?
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