Applying the Concepts and SkillsIn each of Exercises,a. find the regression equation for the data points.b. graph the regression equation and the data points.c. describe the apparent relationship between the two variables under consideration.d. interpret the slope of the regression line.e. identify the predictor and response variables.f. identify outliers and potential influential observations.g. predict the values of the response variable for the specified values of the predictor variable, and interpret your results.Study Time and Score. An instructor at Arizona State University asked a random sample of eight students to record their study times in a beginning calculus course. She then made a table for total hours studied (x) over 2 weeks and test score ( y) at the end of the 2 weeks. Here are the results. For part (g), predict the score of a student who studies for 15 hours. x 10 15 12 20 8 16 14 22 y 92 81 84 74 85 80 84 80
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.
Applying the Concepts and Skills
In each of Exercises,
a. find the regression equation for the data points.
b. graph the regression equation and the data points.
c. describe the apparent relationship between the two variables under consideration.
d. interpret the slope of the regression line.
e. identify the predictor and response variables.
f. identify outliers and potential influential observations.
g. predict the values of the response variable for the specified values of the predictor variable, and interpret your results.
Study Time and Score. An instructor at Arizona State University asked a random sample of eight students to record their study times in a beginning calculus course. She then made a table for total hours studied (x) over 2 weeks and test score ( y) at the end of the 2 weeks. Here are the results. For part (g), predict the score of a student who studies for 15 hours.
| x | 10 | 15 | 12 | 20 | 8 | 16 | 14 | 22 |
| y | 92 | 81 | 84 | 74 | 85 | 80 | 84 | 80 |
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