The following data was collected to explore how the average number of hours a student studies per night and the student's GPA affect their ACT score. The dependent variable is the ACT score, the first independent variable (x1x1) is the number of hours spent studying, and the second independent variable (x2x2) is the student's GPA. Effects on ACT Scores Study Hours GPA ACT Score 55 44 3030 55 33 3030 44 33 2828 22 33 2222 11 22 2020 Step 1 of 2: Find the p-value for the regression equation that fits the given data. Round your answer to four decimal places. Step 2 of 2: Determine if a statistically significant linear relationship exists between the independent and dependent variables at the 0.050.05 level of significance. If the relationship is statistically significant, identify the multiple regression equation that best fits the data, rounding the answers to three decimal places. Otherwise, indicate that there is not enough evidence to show that the relationship is statistically significant.
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.
The following data was collected to explore how the average number of hours a student studies per night and the student's GPA affect their ACT score. The dependent variable is the ACT score, the first independent variable (x1x1) is the number of hours spent studying, and the second independent variable (x2x2) is the student's GPA.
| Study Hours | GPA | ACT Score |
|---|---|---|
| 55 | 44 | 3030 |
| 55 | 33 | 3030 |
| 44 | 33 | 2828 |
| 22 | 33 | 2222 |
| 11 | 22 | 2020 |
Find the p-value for the regression equation that fits the given data. Round your answer to four decimal places.
Determine if a statistically significant linear relationship exists between the independent and dependent variables at the 0.050.05 level of significance. If the relationship is statistically significant, identify the multiple regression equation that best fits the data, rounding the answers to three decimal places. Otherwise, indicate that there is not enough evidence to show that the relationship is statistically significant.
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