Excel Dataset: https://docs.google.com/spreadsheets/d/1GAK-5oTUXyLSNTdSzZrs7MEXWtocYMC2jXcl0jbqW2I/edit?usp=sharing

A new report says closing the digital divide between Indigenous and other Australian students should be part of national Closing the Gap targets. A social scientist randomly sampled 41 government high schools in Australia. For each school, the social scientist recorded the proportion of Indigenous Australians aged 20-24 who had completed Year 12 or equivalent (Year 12 (%)) and the proportion of Indigenous Australians aged 15-19 who were enumerated in a household with internet access (Internet access (%)). Both proportions (Year 12 Completion and Internet Access) are given as a percentage. The 41 observations are recorded in the EXCEL file InternetAccess.xlsx. Research Question: Is there a linear relationship between the Year 12 (%) and Internet access (%)? Download the file for analysing in EXCEL. Assume that the relevant assumptions for linear regression are satisfied and fit a linear regression model to predict the proportion of Year 12 or equivalent completion of Indigenous Australians aged 20-24 (Year 12 (%)). 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 the specified number of decimal places into provided answer space. Figure 1 Figure 2 O 56.5 10 12 55.5 8 Frequency Year 12 (%) 6 54.5 53.5 oo 2 3 33 34 35 36 37 38 39 40 Residuals Internet access (%) Figure 3 00 0 Residuals O CO 33 34 35 36 37 38 39 40 Internet access (%). [1 mark] The slope of the least squares regression line is I. [3 marks] The validity of the statistical inference depend - D To check the linear relationship between the Internet . positive D To check the ndrmalit}.r of residuals, we U59 \"9933\"\"? T. (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 o To check the linear relationship between the Internet access (%) and the Year 12 (%), we use o To check the normality of residuals, we use o To check the residuals in the proportion of Year 12 or equivalent completion of Indigenous A Figure 1 4 (Year 12 (%)) have a constant standard deviation across the range of the Internet access (%), we use Figure 2 3. (1 mark) What else do you see in the scatter plot? Figure 3 4. (1 mark) Based on your answer in Q3, describe how this problem might have occurred? None of these2. (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): o To check the linear relationship between the Internet access (%) and the Year 12 (%), we use o To check the normality of residuals, we use o To check the residuals in the proportion of completion of Indigenous Australians aged 20-24 (Year 12 (%)) have a constant standard deviation across the range of the Internet access (%), we use Figure 1 3. (1 mark) What else do you see in the scatter | Figure 2 4. (1 mark) Based on your answer in Q3, describe Figure 3 night have occurred? None of these2. (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 stateme o To check the linear relationship between the Internet access (%) and the Year 12 (%), we use o To check the normality of residuals, we use o To check the residuals in the proportion of Year 12 or equivalent completion of Indigenous Australians aged 20-24 (Year 12 (%)) have a constant standard deviation across th range of the Internet access (%), we use 3. (1 mark) What else do you see in the scatt 4. (1 mark) Based on your answer in Q3, deso Figure 1 n might have occurred? Figure 2 5. (2 marks) The absolute value of the test st Figure 3 slope of the regression line is: (3dp) with degrees of freedom equal to: [integer). None of these0 3. [1 mark) What else do you see in the scatter plot? 4. (1 mark) Based on your answer in Q3. describe ho A. There is one observation with a relatively large value in Year 12 (96) B. There is one observation with a relatively large value in Internet access ['36) -m equal to (integer) 5. (2 marl-cs) The absolute value of the test statistic o C. There is one observation with a relatively small value in Year 12 ['36) 6' ll mark) The pvalue for testing the slope 0f the r D. There is one observation with a relatively small value in Internet access (96) 7- [2 marl-cs] SElECt the most appropriate conclusion I E. There appears to have two distinct groups. 4. (1 mark) Based on your answer in Q3, describe how this problem might have occurred? 5. (3dp) with degrees of freedom equal to: (integer). A. It may be a data entry error. 6. B. It may be due to random sampling, and we happen not to record other such observations. 7. C. Both A & B predictor for the Year 12 (%)?". D. There may be differences in urban and rural regions.7. (2 marks) Select the most appropriate conclusion to the question "Is the Internet access (%) a useful predictor for the Year 12 (%)?". A. There is a significant negative linear relationship between the Year 12 (%) and the Internet access (%). B. There is not enough evidence to indicate that the Internet access (%) is a useful predictor for the Year 12 (%). C. There is a significant positive linear relationship between the Year 12 (%) and the Internet access (6). 8. (1 mark) The correlation is: (3dp - remember to include a negative sign if appropriate) After checking the potential outlying observation(s) evident in the scatter plot, a new regression model is fitted and the regression results are shown in the table. Answer Questions 9 to 11 based on this table. Regression results on the cleaned data set Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 23.818 4.273 5.574 0 15.167 32.468 Internet access (%) 0.819 0.113 7.282 0 0.592 1.047 9. (2 marks) Use the regression equation to predict the Year 12 (%) completion of Indigenous Australians aged 20-24 with 38.3 Internet access (%): % (3dp) 10. (1 mark) With 95% confidence, we estimate from the data that, on average, for extra one per cent increase in the Internet access (%) is associated with a(n) in the Year 12 (%) completion of Indigenous Australians aged 20-24. A. increase A. increase B. decrease B. decrease C. stay the same C. stay the same 11. (2 marks) The width of the 95% confidence interval associated with an extra one per cent increase in the Internet access (6) is % (3dp) (Hint: Upper Limit - Lower Limit) Copyright @ Macquarie University. Copying or distribution of part or all of the contents in any form is prohibited.5. (2 marks] The absolute value of the test statistic for testing the slope of the regression line is: 6. (1 mark) The p-value for testing the slope of the regression line is less than 0.05. T. (2 marks) Select the most appropriate conclusion to the question "Is the Internet True A. There is a signicant negative linear relationship between the Year 12 ('36) and the In False [Bop] with degrees of freedom equal to: useful predictor for the Year 12 Gilli\". A v ('96)