You may need to use the appropriate technology to answer this question. Do students with higher college grade point averages (GPAs) earn more than those graduates with lower GPAs?† Consider the following hypothetical college GPA and salary data (10 years after graduation). GPA Salary ($) 2.22 72,000 2.27 48,000 2.57 72,000 2.59 62,000 2.77 86,000 2.85 98,000 3.12 133,000 3.35 130,000 3.66 157,000 3.68 162,000 (a) Develop a scatter diagram for these data with college GPA as the independent variable. A scatter diagram has a horizontal axis labeled "GPA" with values from 2 to 4 and a vertical axis labeled "Salary ($)" with values from 0 to 180,000. The scatter diagram has 10 points. A pattern goes down and right from (2.22, 122,000) to (3.68, 8,000). The points are scattered moderately from the pattern. A scatter diagram has a horizontal axis labeled "GPA" with values from 2 to 4 and a vertical axis labeled "Salary ($)" with values from 0 to 180,000. The scatter diagram has 10 points. A pattern goes up and right from (2.22, 8,000) to (3.68, 122,000). The points are scattered moderately from the pattern. A scatter diagram has a horizontal axis labeled "GPA" with values from 2 to 4 and a vertical axis labeled "Salary ($)" with values from 0 to 180,000. The scatter diagram has 10 points. A pattern goes down and right from (2.22, 162,000) to (3.68, 48,000). The points are scattered moderately from the pattern. A scatter diagram has a horizontal axis labeled "GPA" with values from 2 to 4 and a vertical axis labeled "Salary ($)" with values from 0 to 180,000. The scatter diagram has 10 points. A pattern goes up and right from (2.22, 48,000) to (3.68, 162,000). The points are scattered moderately from the pattern. What does the scatter diagram indicate about the relationship between the two variables? The scatter diagram indicates a positive linear relationship between GPA and salary.The scatter diagram indicates no apparent relationship between GPA and salary. The scatter diagram indicates a nonlinear relationship between GPA and salary.The scatter diagram indicates a negative linear relationship between GPA and salary. (b) Use these data to develop an estimated regression equation that can be used to predict annual salary 10 years after graduation given college GPA. (Let x = GPA, and let y = salary (in $). Round your numerical values to the nearest integer.) ŷ = (c) At the 0.05 level of significance, does there appear to be a significant statistical relationship between the two variables? (Use the F test.) State the null and alternative hypotheses. H0: ?0 ≠ 0 Ha: ?0 = 0H0: ?0 = 0 Ha: ?0 ≠ 0 H0: ?1 = 0 Ha: ?1 ≠ 0H0: ?1 ≥ 0 Ha: ?1 < 0H0: ?1 ≠ 0 Ha: ?1 = 0 Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to three decimal places.) p-value = State your conclusion. Reject H0. There is not a significant statistical relationship between GPA and salary.Reject H0. There is a significant statistical relationship between GPA and salary. Do not reject H0. There is a significant statistical relationship between GPA and salary.Do not reject H0. There is not a significant statistical relationship between GPA and salary.
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
GPA | Salary ($) |
---|---|
2.22 | 72,000 |
2.27 | 48,000 |
2.57 | 72,000 |
2.59 | 62,000 |
2.77 | 86,000 |
2.85 | 98,000 |
3.12 | 133,000 |
3.35 | 130,000 |
3.66 | 157,000 |
3.68 | 162,000 |
Ha: ?0 = 0H0: ?0 = 0
Ha: ?0 ≠ 0 H0: ?1 = 0
Ha: ?1 ≠ 0H0: ?1 ≥ 0
Ha: ?1 < 0H0: ?1 ≠ 0
Ha: ?1 = 0
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