The best predicted height of an opponent given that the president had a height of 183 cm is _________ cm. How close is the result to the actual opponent height of 185 cm ? a. The result is within 5 cm of the actual opponent height of 185 cm.b. The result is more than 5 cm greater than the actual opponent height of 185 cm.c. The result is more than 5 cm less than the actual opponent height of 185 cm.d. The result is excatly the same as the actual opponent height of 185 cm. Listed below are the heights (cm) of winning presidential candidates and their main opponents from several recent presidential elections. Find the regression equation,letting president be the predictor (x) variable. Find the best predicted height of an opponent given that the president had a height of 183 cm. How close is the result tothe actual opponent height of 185 cm?President 175 188 177 191 183 185 183 192 188Opponent173 188 183 169 182 177 185 180 173CHThe regression equation is ŷ = + (x.(Round the y-intercept to the nearest integer as needed. Round the slope to three decimal places as needed.)

The regression equation is obtained by using the formula : ŷ= a + bx ... (1) Where, a = y-intercept and b = slope. Formula to calculate y-intercept : a = ȳ – b1(x̄) ...(2) Formula to calculate slope : b = Σ(x – x̄)(y – ȳ)/Σ(x – x̄)2 ... (3)Let x represents president height and y represents opponent height. n = number of observations. n = 9 Mean of x values : x̄ = Σx /n (Σx provided below in the table) x̄ = 1662/9 x̄ = 184.66667 Mean of y values : ȳ = Σy/n (Σy provided below in the table) ȳ = 1610/9 ȳ = 178.88889 x y x–x̄ y–ȳ (x–x̄)2 (x–x̄)(y–ȳ) 175 173 –9.66667 –5.88889 93.44451 56.92596 188 188 3.33333 9.11111 11.11109 30.37034 177 183 –7.66667 4.11111 58.77783 –31.51852 191 169 6.33333 –9.88889 40.11107 –62.62960 183 182 –1.66667 3.11111 2.77779 —5.18519 185 177 0.33333 –1.88889 0.11111 –0.62962 183 185 –1.66667 6.11111 2.77779 –10.18520 192 180 7.33333 1.11111 53.77773 8.14814 188 173 3.33333 –5.88889 11.11109 –19.62961 Σx = 1662 Σy = 1610 Σ(x–x̄)2 = 274.00001 Σ(x–x̄)(y–ȳ) = –34.3333 Slope (b) of the regression equation : Using (3) from the step 1 we have, b = Σ(x – x̄)(y – ȳ)/Σ(x – x̄)2 On substituting the values from the table provided in step 2 we get, b = (–34.3333)/274.00001 (rounded to 3 decimal places) b = –0.125 Intercept (a) of the regression equation : Using (2) from the step 1, a = ȳ – b × x̄ On substituting the values we get, a = 178.88889 – (–0.1253) × 184.66667 a = 178.88889 + 23.13873 a = 202.02762 Rounding to the nearest integer we get, a = 202 Regression equation : Using (1) from the step 1, ŷ= a + bx ŷ = 202 + (–0.125)x (ANSWER) The best predicted height of an opponent given that the president had a height of 183 cm is calculated as follows : Substitute , x = 183 in the calculated regression equation, ŷ = 202 – 0.125 × 183 ŷ = 202 – 22.875 ŷ = 179.125 ANSWER : The best predicted height of an opponent given that the president had a height of 183 cm is 179.125 cm. For the president height of 183 cm, heights of an opponent are as follows, Actual height = 185 cm Predicted height = 179.125 cm Difference = (Actual height – Predicted height) Difference =(185 – 179.125) cm = 5.875 cm Since, the difference is greater than 5 cm i.e., 5.875 cm > 5 cm. The predicted height is more than 5 less than the actual height. The correct option is c. ANSWER : c. The result is more than 5 cm less than the actual opponent height of 185 cm.