An academic is interested in whether international collaboration, measured by the international co-publication rate, is associated with a higher quality of scientific work, measured by the relative impact factor of the publication. The EXCEL file InternationalCollaborations.xisx contains the international co-publication rate and the relative impact factor of 36 randomly sampled journal articles, and this is Sample A. Research Question: "Is there a linear relationship between the international co-publication rate and the relative impact factor of the publication?" Download the file for analysing in EXCEL. Assume the relevant assumptions for linear regression are satisfied and fit a linear regression model to predict the publication's relative impact factor from its international co-publication rate. Use your Excel output and any other information provided to answer the following questions. For each question, either choose a correct option or type a numerical value with a specified number of decimal places into provided answer space. Figure 1 Figure 2 2 0 0.2 0.4 0.6 0.8 Relative impact factor Frequency Boo O 0.8 -0.6 -0.4 0.2 0.0 0.2 0.4 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Residuals international co-publication rate Figure 3 O O O O O O Residuals -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.2 0.3 0.4 0.5 0.6 0,7 0.8 international co-publication rate 1. (1 mark) The slope of the least squares regression line is0 3. (1 mark) What else do you see in the scatter plot? 4. (1 mark; Based on your answer in Q3. describe how this problem might have occurred? 5. (2 marks} The absolute value of the test statistic for testing the slope of the regression line is: {3dp) with degrees of freedom equal to: 6. (1 mark} The pwalue for testing the slope of the regression line is less than 0.05. 7. (2 marks) Select the most appropriate conclusion to the question "ls the international co-publication rate a useful predictor for the Relative impact factor?". A v A. There is a signilirant negative linear relationship between the Relative impact factor and international co-publioation rate. B. There is not enough evidence to indicate that international co-publiration rate is a useful predictor for the Relative impact factor. C. There is a signilioant positive linear relationship between the Relative impacl factor and international co-publioation rate. 8. (1 mark} The correlation (r) is: (3dp , remember to include a negative sign if appropriate) (integer). 0 The academic obtained a new sample (Sample B) and fitted a second regression model. The ANOVA table and the regression results are shown below. ANOVA df SS MS F Significance F Regression 1 0.08 0.08 3.527 0.069 Residual 33 0.77 0.023 Total 34 0.85 Regression results on Sample B Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 0.287 0.098 2.915 0.006 0.087 0.487 international co-publication rate 0.283 0.150 1.878 0.069 -0.023 0.588 9. (2 marks) What is the coefficient of determination (R2) of the regression model for Sample B? (3dp) (Hint: Enter your answer as a decimal, such as 0.01) 10. (1 mark) Which sample (Sample A versus Sample B) has a better model fit? A. Sample A B. Sample B C. Neither Sample A nor Sample B D. Insufficient information to make a decision