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.xlsx 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 publications 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. (1 mark) The slope of the least squares regression line is Answer 1 Question 1 positive (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): To check the linear relationship between the international co-publication rate and the Relative impact factor, we use Answer 2 Question 1 Figure 2 To check the normality of residuals, we use Answer 3 Question 1 Figure 1 To check the residuals in the Relative impact factor have a constant standard deviation across the range of international co-publication rate values, we use Answer 4 Question 1 Figure 3 (1 mark) What else do you see in the scatter plot? Answer 5 Question 1 (1 mark) Based on your answer in Q3, describe how this problem might have occurred? Answer 6 Question 1 (2 marks) The absolute value of the test statistic for testing the slope of the regression line is: Answer 7 Question 1 (3dp) with degrees of freedom equal to: Answer 8 Question 1 (integer). (1 mark) The p-value for testing the slope of the regression line is less than 0.05. Answer 9 Question 1 (2 marks) Select the most appropriate conclusion to the question Is the international co-publication rate a useful predictor for the Relative impact factor?. Answer 10 Question 1 A. There is a significant negative linear relationship between the Relative impact factor and international co-publication rate. B. There is not enough evidence to indicate that international co-publication 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 co-publication rate. (1 mark) The correlation (r ) is: Answer 11 Question 1 (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 0.145 0.145 3.389 0.074 Residual 33 1.451 0.043 Total 34 1.596 Regression results on Sample B Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 0.799 0.139 5.751 0.000 0.517 1.081 international co-publication rate 0.338 0.184 1.841 0.074 -0.035 0.711 (2 marks) What is the coefficient of determination (R2 ) of the regression model for Sample B? Answer 12 Question 1 (3dp) (Hint: Enter your answer as a decimal, such as 0.01) (1 mark) Which sample (Sample A versus Sample B) has a better model fit? Answer 13 Question 1 A. Sample A B. Sample B C. Neither Sample A nor Sample B D. Insufficient information to make a decision