Given the data below, find the equation of the regression line with height as the explanatory variable and use the regression line to find the predicted values for x = 68 inches and x = 72 inches. Height in inches 69, 67, 69, 71, 70, 72 Weight in lbs 164,

To find the equation of the regression line, we first need to calculate the correlation coefficient, r, and the slope, b. r = (n?xy - ?x?y)/(?(n?x^2 - (?x)^2) * ?(n?y^2 - (?y)^2)) where n = number of observations, ? = sum, and x and y represent height and weight, respectively. n = 6 ?x = 418 ?y = 1088 ?xy = 20008 ?x^2 = 28966 ?y^2 = 384876 Substituting these values into the formula, we get: r = (6(20008) - (418)(1088))/?((6(28966) - (418)^2) * (6(384876) - (1088)^2)) r = 0.906 Since r is positive and close to 1, there is a strong positive linear correlation between height and weight. The slope of the regression line is given by: b = r(?(n?y^2 - (?y)^2)/?(n?x^2 - (?x)^2)) b = 2.696 The equation of the regression line is therefore: weight = 114.373 + 2.696(height) Using this equation, we can find the predicted weight for a given height. For x = 68 inches: weight = 114.373 + 2.696(68) = 185.381 lbs For x = 72 inches: weight = 114.373 + 2.696(72) = 196.069 lbs Therefore, the predicted weight for a person with a height of 68 inches is 185.381 lbs, and the predicted weight for a person with a height of 72 inches is 196.069 lbs.