The second slide is the first part of the question and the first slide is the second part of the question. **Transcription for Educational Website****Title: Analysis of GPA and Salary Relationship****Introduction:**This section explores whether students with higher college grade point averages (GPAs) earn more than those with lower GPAs. The data presented considers hypothetical college GPA and salary information, collected 10 years post-graduation.**Data Table:**| GPA | Salary ($) ||-----|------------|| 3.68| 162,000 || 3.15| 157,000 || 3.12| 130,000 || 2.77| 98,000 || 2.59| 72,000 || 2.27| 62,000 || 2.22| 48,000 |**Task:**(a) Develop a scatter diagram for these data points with college GPA as the independent variable.**Scatter Plots:**Four different scatter plots are displayed, each representing the relationship between GPA and Salary. The vertical axis represents Salary ($), ranging from $20,000 to $180,000, while the horizontal axis represents GPA, ranging from 2.0 to 4.0.**Questions:**1. What does the scatter diagram indicate about the relationship between the two variables? - **Option A**: The scatter diagram indicates a positive linear relationship between GPA and salary. - **Option B**: The scatter diagram indicates a negative linear relationship between GPA and salary. - **Option C**: The scatter diagram indicates no apparent relationship between GPA and salary.**Analysis:**Students are encouraged to examine the scatter plots closely and determine the nature of the relationship between GPA and salary based on the distribution of data points. This exercise aims to develop students' analytical skills in interpreting data visually.**Conclusion:**Understanding the relationship between academic performance and financial outcomes can provide valuable insights for students in planning their educational and career paths. ## Transcription for Educational Use### Assessment of Statistical Significance in Regression AnalysisThis educational exercise involves using regression analysis to predict annual salary 10 years after graduation based on college GPA.#### Steps for Analysis:1. **Develop the Regression Equation:** - Utilize the available data to form an estimated regression equation for predicting the annual salary. - Let $ x = \text{GPA} $ and $ y = \text{salary (in \$)} $. - Ensure all numerical values are rounded to the nearest integer.2. **Hypothesis Testing:** - **At the 0.05 level of significance**, determine whether there is a significant statistical relationship between GPA and salary. - Use the F-test to assess this relationship.3. **State the Null $(H_0)$ and Alternative $(H_a)$ Hypotheses:** - Choose one of the following to set as the hypotheses: - $ H_0: \beta_1 = 0 $ - $ H_a: \beta_1 \neq 0 $ - $ H_a: \beta_1 > 0 $ - $ H_a: \beta_1 < 0 $4. **Calculate the Test Statistic:** - Find the value of the test statistic, rounding your answer to two decimal places.5. **Determine the P-Value:** - Calculate the p-value, ensuring to round your answer to three decimal places.6. **Conclusion:** - Based on the findings, make a conclusion: - Do not reject $ H_0 $: There is not a significant statistical relationship between GPA and salary. - Reject $ H_0 $: There is a significant statistical relationship between GPA and salary.Follow these steps to analyze whether there is a significant link between GPA and future salary, thereby illustrating the practical application of statistical analysis in educational research and career predictions.

Name: The second slide is the first part of the question and the first slid
Uploaded: 2024-03-05T11:53:49.000Z
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Description: The second slide is the first part of the question and the first slide is the second part of the question. **Transcription for Educational Website****Title: Analysis of GPA and Salary Relationship****Introduction:**This section explores whether stud

We are given the data for grade point averages (GPA) and salary for the 10 students. We need to test whether the students with higher college GPA earn more than those graduates with lower GPAs. We use an excel to plot the scatter plot as well as to fit linear regression equation for the given data. To plot the scatter diagram in excel we follow the path below; Enter the data in excel sheet >>> Select the data >>> go to Insert menu >>> Charts >>> Insert scatter (X,Y) Plotting the scatter diagram in excel we get option C is correct for part A. - The graph shows that there is positive linear relationship between GPA and salary. While to fit the linear regression equation for the given data follow the path below; Enter the data in excel sheet >>> Go to Data menu >>> Data Analysis >>> Regression >>> Input Y-values and X-values >>> Select the output range >>> Click on OK This gives the output for the fit the linear regression equation for the given data as below; The estimates for the regression coefficient are given in the column "Coefficients" of the output. These are given by, a = 113300 (rounded value) and b = 74106 (rounded value). This gives, y^=a+b*x=113300+74106*x. To test the significance of statistical relation between GPA and salary we check whether the slope coefficient is significantly different than 0. For this purpose we use F test. The null and alternative hypothesis in this case are as follows; H0 : β1=0 Vs Ha : β1≠0 The value of the statistic value is given in the column "F" of ANOVA table. This gives, F-stat = 104.57 (rounded value). The p-value corresponding to this is given in the column "Significance F" of ANOVA table. This gives, p-value = 0.000007183 ≈ 0.000 = 0 (rounded value). The decision rule based on p-value is given as follows; If p-value ≤ α (significance level) then we reject the null hypothesis and conclude that there is significant relationship between GPA and salary. If p-value > α (significance level) then we fail to reject the null hypothesis and conclude that there is not significant relationship between GPA and salary. Here p-value = 0 and significance level (α) = 0.05, this gives p-value < α. Hence we reject the null hypothesis and conclude that there is significant relationship between GPA and salary.