The objective of this question is to show how R can be applied in the context...

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The objective of this question is to show how R can be applied in the context of linear regression using matrices. Given n pairs of values {(₁, 1), (2, 32). (En, yn)), the sample (Pearson) correlation coefficient r is defined by Σ(x-2)(y-7) im1 72 72 Σ(x; - z), Σ( – g)" i=1 T= 71 The cor () function can input two vector arguments of the same length and output the correlation coefficient between them. Write a function called my_cor () that computes the correlation between two numeric vectors x and y without the cor (), cov(), var(), or sd() functions. Include a character argument called use that specifies whether to use all observations (use = "everything") or only pairwise complete observations (use = "pairwise.complete.obs") by removing a pair (ri, yi) if either r, or y; is missing. The output of my_cor (x, y) and cor(x, y) should be identical for any numeric vectors x and y. Hint: The cor() function also allows for matrix inputs x and y and computes the correlation matrix between columns of x and columns of y. Your my_cor () function does not need to include this functionality. (b) Assume there is a linear relationship between variables x and y. The least squares regression line is a linear model that predicts y from z. The equation of the regression line is denoted by y = a + bx. The coefficients of the regression line are computed by the formulas Sy b=r- and a=ỹ - ba, where I and ÿ and the respective means and s, and sy are the respective standard deviations for the data vectors x and y. Write a function called linreg() that inputs two numeric vectors x and y and outputs a numeric vector of length 2 that corresponds to the coefficients a and b of the least squares regression line that predicts y from x. Include a character argument called use that specifies whether to use all observations (use = "everything") or only pairwise complete observations (use = "pairwise.complete.obs") by removing a pair (*i, y₁) if either z, or y; is missing. The objective of this question is to show how R can be applied in the context of linear regression using matrices. Given n pairs of values {(₁, 1), (2, 32). (En, yn)), the sample (Pearson) correlation coefficient r is defined by Σ(x-2)(y-7) im1 72 72 Σ(x; - z), Σ( – g)" i=1 T= 71 The cor () function can input two vector arguments of the same length and output the correlation coefficient between them. Write a function called my_cor () that computes the correlation between two numeric vectors x and y without the cor (), cov(), var(), or sd() functions. Include a character argument called use that specifies whether to use all observations (use = "everything") or only pairwise complete observations (use = "pairwise.complete.obs") by removing a pair (ri, yi) if either r, or y; is missing. The output of my_cor (x, y) and cor(x, y) should be identical for any numeric vectors x and y. Hint: The cor() function also allows for matrix inputs x and y and computes the correlation matrix between columns of x and columns of y. Your my_cor () function does not need to include this functionality. (b) Assume there is a linear relationship between variables x and y. The least squares regression line is a linear model that predicts y from z. The equation of the regression line is denoted by y = a + bx. The coefficients of the regression line are computed by the formulas Sy b=r- and a=ỹ - ba, where I and ÿ and the respective means and s, and sy are the respective standard deviations for the data vectors x and y. Write a function called linreg() that inputs two numeric vectors x and y and outputs a numeric vector of length 2 that corresponds to the coefficients a and b of the least squares regression line that predicts y from x. Include a character argument called use that specifies whether to use all observations (use = "everything") or only pairwise complete observations (use = "pairwise.complete.obs") by removing a pair (*i, y₁) if either z, or y; is missing.

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a Here is a function in R that computes the correlation coefficient between two n... View the full answer