This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here are the solutions to your questions. i) Plot the scattered diagram for the data To plot a scattered diagram, you will represent each pair of data points (x, y) as a single point on a graph. Let the Advert cost (x) be on the horizontal axis and Sales (y) be on the vertical axis. The data points are: (6, 21) (10, 28) (12, 34) (11, 31) (13, 40) Plot these five points on a coordinate plane. The resulting graph will show the relationship between advert cost and sales. ii) Determine the sample correlation coefficient (r) Step 1: Calculate the necessary sums. Let x be Advert cost and y be Sales. |c|c|c|c|c| x & y & xy & x^2 & y^2 \\ 6 & 21 & 126 & 36 & 441 \\ 10 & 28 & 280 & 100 & 784 \\ 12 & 34 & 408 & 144 & 1156 \\ 11 & 31 & 341 & 121 & 961 \\ 13 & 40 & 520 & 169 & 1600 \\ x = 52 & y = 154 & xy = 1675 & x^2 = 570 & y^2 = 4942 \\ The number of data points is n=5. Step 2: Apply the formula for the sample correlation coefficient. The formula for r is: r = (n xy - ( x)( y))/(sqrt([n x^2 - ( x)^2][n y^2 - ( y)^2])) Step 3: Substitute the calculated sums into the formula. r = (5(1675) - (52)(154))/(sqrt([5(570) - (52)^2][5(4942) - (154)^2])) Step 4: Perform the calculations. Numerator: 5(1675) - (52)(154) = 8375 - 8008 = 367 Denominator, first part: 5(570) - (52)^2 = 2850 - 2704 = 146 Denominator, second part: 5(4942) - (154)^2 = 24710 - 23716 = 994 Denominator: sqrt((146)(994)) = sqrt(145024) ≈ 380.82016 Calculate r: r = (367)/(380.82016) ≈ 0.9637 The sample correlation coefficient is 0.9637. iii) Find the coefficient of determination (r^2) Step 1: Square the value of the correlation coefficient (r) found in part (ii). r^2 = (0.9637)^2 Step 2: Calculate the value. r^2 ≈ 0.9287 The coefficient of determination is 0.9287. Send me the next one 📸