Question

Find the regression equation letting overhead with be the predictor(s) variable. Find the best predicted weight of a seal the overhead width moured from a photograph is 16 cm. Can the prediction be correct? What is wrong with predicting the weight in this case? Use a significance level of 0.05. Overhead Width (cm) 84 79 82 7.8 Weight (kg) 201 209 190 181 200 Click the loon to view the critical values of the Pearson correlation coeficient The regression equation is = D.Ox (Round to one decimal place as meded) The best predicted weight for an overhead width of 16 cm isk (Round to one decimal place as needed) Can the prediction be correct? What is wrong with predicting the weight in this case? OA The prediction cannot be correct because a negative weight does not make sense and because there is not suficient evidence of a new correlation OB. The prediction cannot be correct because there is not sufficient evidence of a linear correlation. The width in this case is beyond the scope of the available sample data OC. The prediction cannot be correct because a negative weight does not make sense. The within this case is beyond the scope of the available sample data OD. The prediction can be correct. There is nothing wrong with predicting the weight in this case

Answer 1

Solution :

Given that, Overhead width x as 8.4,7.9,9.5,8.2,7.5,7.8

Weight y as 201,209,274,190,181,200

=> The regression equation is y^ = -144.0 + 43.0*x (rounded)

Explanation: We will find an equation of the regression line in 4 steps. Step 1: Find X Y and X as it was done in the table below. X 8.4 7.9 9.5 201 209 274 X Y 1688.4 1651.1 2603 1558 1357.5 1560 XX 70.56 62.41 90 25 67.24 56.25 E0.84 190 8.2 7.5 7.8 181 200 Step 2: Find the sum of every column: ΣΚ = 49.3, ΣΥ= 1255, ΣΧΥ = 10418, ΣΧ2 = 407.55 Step 3: Use the following equations to find a and b. Ο Ε ΣΥΣΧ2 –ΣΧ·ΣΧΥ η ΣΧ2 – (Σκ) 1255 - 407.55 – 49.3 • 10418 6 - 407.55 – 4932 8 -143.967 • ΣΧΥ -ΣΧΣΥ ΣΧ2 – (Σκ)2 Step 4: Substitute a and bin regression equation formula 6 • 10418 – 49.3. 1255 6 - 407.55 – (49.3) & 42.978 3 = α + 5. α - - 143.967 + 42.978-8

=> The best predicted weight for an overhead width of 1.6 cm is

=> y^ = -144.0 + 43.0*1.6

= -75.2

=> Option C. The prediction cannot be correct because a negative weight does not make sense. The width in this case is beyond the scope of the available sample data.