(a) Explain the difference between the line y = a + ẞx and the line ŷ = a + bx. y is the equation of the population regression line, which relates the mean value of y to the value of x, whereas ŷ is the equation of an estimated regression line, which is an estimate of the population regression line obtained from a particular set of (x, y) observations. y is the equation of the sample regression line, which relates the mean value of y to the value of x, whereas ŷ is the equation of an estimated regression line, which is an estimate of the sample regression line obtained from a particular set of (x, y) observations. ŷ is the equation of the population regression line, which relates the mean value of y to the value of x, whereas y is the equation of an estimated regression line, which is an estimate of the population regression line obtained from a particular set of (x, y) observations. Oŷ is the equation of the sample regression line, which relates the mean value of y to the value of x, whereas y is the equation of an estimated regression line, which is an estimate of the sample regression line obtained from a particular set of (x, y) observations. There is no difference between y and ŷ. (b) Explain the difference between ẞ and b. ẞ is the slope of the sample regression line, whereas b is an estimate of ẞ obtained from a particular set of (x, y) observations. ẞ is the slope of the population regression line, whereas b is an estimate of ẞ obtained from a particular set of (x, y) observations. There is no difference between ẞ and b. b is the slope of the population regression line, whereas ẞ is an estimate of b obtained from a particular set of (x, y) observations. b is the slope of the sample regression line, whereas ẞ is an estimate of b obtained from a particular set of (x, y) observations. (c) Let x* denote a particular value of the independent variable. Explain the difference between a + ẞx* and a + bx*. a + ẞx* is the mean value of y when x = x*, whereas a + bx* is an estimate of the mean value of y, when x = x*. a + bx* is the mean value of y when x = x*, whereas a + ẞx* is an estimate of the mean value of y, when x = x*. There is not difference between a + ẞx* and a + bx*. a + bx* is the mean value of x when y = y*, whereas α + ẞx* is an estimate of the mean value of x, when y = y*. aẞx is the mean value of y when y = y*, whereas a + bx* is an estimate of the mean value of x, when y = y*. (d) Explain the difference between σ and se Se is the shared standard deviation of the y distributions based on a + ẞx, whereas σ is an estimate of s obtained from a particular set of (x, y) observations. There is not difference between σ and se. e Se is the shared standard deviation of the y distributions based on a + bx, whereas σ is an estimate of s obtained from a particular set of (x, y) observations. ☞ is the shared standard deviation of the y distributions based on a + ẞx, whereas så is an estimate of σ obtained from a particular set of (x, y) observations. σ is the shared standard deviation of the y distributions based on a + bx, whereas s is an estimate of σ obtained from a particular set of (x, y) observations. Se