x = stress score on morning of test; y = grade on test x: 4 7 9 10 6 6 y: 96 89 63 58 94 86 a) Draw a scatterplot in space below. b) Determine the value of r. ________________ c) Give the direction and strength of the correlation. _____________________________ d) Find the equation of the regression line. __________________________ e) Predict the grade for a student with stress level 7. ____________ f) Use the result of e) to find the residual for the data point (7,89). ___________ g) Circle the correct choice and fill in the blank: For each additional point on the stress score, the grade for a student (increases, decreas
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.
Data were collected from 6 students:
x = stress score on morning of test; y = grade on test
x: 4 7 9 10 6 6
y: 96 89 63 58 94 86
a) Draw a
b) Determine the value of r. ________________
c) Give the direction and strength of the
d) Find the equation of the regression line. __________________________
e) Predict the grade for a student with stress level 7. ____________
f) Use the result of e) to find the residual for the data point (7,89). ___________
g) Circle the correct choice and fill in the blank: For each additional point on the
stress score, the grade for a student (increases, decreases) on average by about
_______ points.
h) Fill in the blank: ______ % of the variation in grades can be explained by the
stress score.
i) Fred’s stress score was 2. Will the regression equation accurately predict his
grade? Explain.
j) It turned out that, for the six students sampled, the correlation between the
number of hours spent studying and the grade was r = +.533. Would knowing the number
of hours studied give a better prediction on the grade than knowing the stress level?
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