There is a correlation study about the relationship between the amount of dietary protein intake in a day (x, in grams) and the systolic blood pressure (y, in mmHg) of middle-aged adults. In total, 90 adults participated in the study. You are given the following summary statistics and the Excel output after performing correlation and regression.

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Summary Statistics Sum of squares ofx data = 288,241 Sum of squares of y data = 1,511,545 Sum of x data = 5,027 Sum of y data = 11,621 Sum products of x and y = 640,890 Maximum value ofx 72 Minimum value ofx= 40 Protein BP Protein 1 BP -0.90568 Output 1: Correlation analysis on x and y variables SUMMARY OUTPUT Regression Statisties Multiple R R Square Adjusted R Square Standard Error Observations 0.905677607 0.820251929 0.818209337 4.743467805 90 ANOVA Significance F 1.49853E-34 S5 MS Regression Residual Total 9035.612716 9035.613 401.5741 88 1980.04284 22.50049 89 11015.65556 Coefficients Standard Error t Stat Pvalue Lower 95N Upper 95N Lower 95.0% Upper 95.ON Intercept 190.6141057 3.109032032 61.30979 5.57E-74 184.4355579 196.7926536 184.4355579 196.7926536 0.05493746 -20.0393 1.5E-34 -1.210085651 -0.991732338 -1.210085651 -0.991732338 Protein Output 2: Regression analysis on x and y variables (with some information missing) a) Write down the correlation coefficient between the two variables. Interpret the answer in the context of the subject matter. (3 marks) b) Find the slope of the regression line. Hence, write down the equation of the regression line. (3 marks) c) Interpret the slope of the regression line. Make sure your answer is written in the context of the subject matter. (2 marks) d) Do you think it is accurate to use the regression line to estimate the systolic blood pressure of a middle-aged adult whose dietary protein intake in a day is 80 grams per day? Explain your answer. (2 marks) Summary Statistics Sum of squares ofx data = 288,241 Sum of squares of y data = 1,511,545 Sum of x data = 5,027 Sum of y data = 11,621 Sum products of x and y = 640,890 Maximum value ofx 72 Minimum value ofx= 40 Protein BP Protein 1 BP -0.90568 Output 1: Correlation analysis on x and y variables SUMMARY OUTPUT Regression Statisties Multiple R R Square Adjusted R Square Standard Error Observations 0.905677607 0.820251929 0.818209337 4.743467805 90 ANOVA Significance F 1.49853E-34 S5 MS Regression Residual Total 9035.612716 9035.613 401.5741 88 1980.04284 22.50049 89 11015.65556 Coefficients Standard Error t Stat Pvalue Lower 95N Upper 95N Lower 95.0% Upper 95.ON Intercept 190.6141057 3.109032032 61.30979 5.57E-74 184.4355579 196.7926536 184.4355579 196.7926536 0.05493746 -20.0393 1.5E-34 -1.210085651 -0.991732338 -1.210085651 -0.991732338 Protein Output 2: Regression analysis on x and y variables (with some information missing) a) Write down the correlation coefficient between the two variables. Interpret the answer in the context of the subject matter. (3 marks) b) Find the slope of the regression line. Hence, write down the equation of the regression line. (3 marks) c) Interpret the slope of the regression line. Make sure your answer is written in the context of the subject matter. (2 marks) d) Do you think it is accurate to use the regression line to estimate the systolic blood pressure of a middle-aged adult whose dietary protein intake in a day is 80 grams per day? Explain your answer. (2 marks)

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