An academic is interested in whether International collaboration, measured by the international copublication rate, is associated with a higher quality of scientific work, measured by the relative impact factor of the publication. The EXCEL file InternationalCollaborations.xlsx contains the international copu blication rate and the relative impact factor of 41 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 copublication 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. \fFigure 3 O 0.0 0.2 0.4 0.6 0.8 Residuals O O O OO O O O O b Oo oo O OO O O O O -0.4 0.2 0.4 0.6 0.8 1.0 international co-publication rate1. {1 mark) The slope of the least squares regression line is 2. {3 marks) The validity of the statistical inference depends on how well the data approximates the assumptions of the linear model (choose the figure that goes with each statement): 0 To check the linear relationship between the international copublication rate and the Relative impact factorI we use A v 0 To check the normality of residuals, we use 0 To check the residuals in the Relative impact factor have a constant standard deviation across the range of international copublication rate values, we use : 3. {1 mark) What else do you see in the scatter plot? 0 4. {1 mark) Based on your answer in Q3, describe how this problem might have occurred? 0 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: (integer). A 6. (1 mark) The pvalue for testing the slope of the regression line is less than 0.05. v 7. (2 marks) Select the most appropriate conclusion to the question "Is the international copublication rate a useful predictor for the Relative impact factor?". A. There is a significant negative linear relationship between the Relative impact factor and international copu blication rate. B. There is not enough evidence to indicate that international copublication rate is a useful predictor for the Relative impact factor. C. There is a significant positive linear relationship between the Relative impact factor and international copublication rate. 8. (1 mark) The correlation (r) is: (3dp remember to include a negative sign if appropriate) 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 0.063 0.063 2.021 0.163 Residual 38 1.221 0.031 Total 39 1.284 Regression results on Sample B Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 0.297 0.118 2.513 0.016 0.058 0.536 international co-publication rate 0.208 0.146 1.422 0.163 -0.088 0.5049. (2 marks) What is the coefficient of determination (R) 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