A marketing professor at Givens College is interested in the relationship between hours spent studying and total points earned in a course. Data collected on 10 students who took the course last quarter follow. Hours Spent Studying Total Points Earned 45 40 30 35 90 75 60 65 105 90 65 50 90 90 80 80 55 45 75 65
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.
A marketing professor at Givens College is interested in the relationship between hours spent studying and total points earned in a course. Data collected on 10 students who took the course last quarter follow.
| Hours Spent Studying |
Total Points Earned |
|---|---|
| 45 | 40 |
| 30 | 35 |
| 90 | 75 |
| 60 | 65 |
| 105 | 90 |
| 65 | 50 |
| 90 | 90 |
| 80 | 80 |
| 55 | 45 |
| 75 | 65 |
(a)Develop an estimated regression equation showing how total points earned can be predicted from hours spent studying. (Round your numerical values to two decimal places.)
ŷ =
(b) Test the significance of the model with ? = 0.05. (Use the F test.)
=
State the null and alternative hypotheses.
H0: ?0 = 0
Ha: ?0 ≠ 0
H0: ?1 ≥ 0
Ha: ?1 < 0
H0: ?1 = 0
Ha: ?1 ≠ 0
H0: ?1 ≠ 0
Ha: ?1 = 0
H0: ?0 ≠ 0
Ha: ?0 = 0
Find the value of the test statistic. (Round your answer to two decimal places.)
=
Find the p-value. (Round your answer to three decimal places.)
p-value =
State your conclusion.
(A) Do not reject H0. We conclude that the relationship between hours spent studying and total points earned is significant.
(B) Do not reject H0. We cannot conclude that the relationship between hours spent studying and total points earned is significant.
(C) Reject H0. We cannot conclude that the relationship between hours spent studying and total points earned is significant.
(D) Reject H0. We conclude that the relationship between hours spent studying and total points earned is significant.
(c) Predict the total points earned by Mark Sweeney. He spent 100 hours studying. (Round your answer to two decimal places.)
____ points
(d) Develop a 95% prediction interval for the total points earned by Mark Sweeney. (Round your answers to two decimal places.)
____ points to _____ points
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