Question

11. Use the following table to answer the questions Х Y 7 18 8 23 10 28 13 32 14 37 16 41 20 45 26 52 a. Make a scatterplot and determine the relationship between X and Y b. Find the linear regression equation Y1 = (round a and b to the nearest hundredth ) c. Find r and to the nearest hundredth d. Use the equation found in part b to determine X to the nearest whole number when Y' = 60

Answer 1

ANSWER

65 60 55 50 45 40 35 30 25 20 15 10 2 468 10 12 14 16 18 20 22 24 26 28 30

(b)

Step 1: Find X · Y and X2 as it was done in the table below. Y Χ.Υ X X X 7 18 126 49 8 23 184 64 10 28 280 100 13 32 416 169 14 37 518 196 16 41 256 656 900 20 45 400 26 52 1352 676 Step 2: Find the sum of every column: ΣΧ = 114, ΣΥ = 276, ΣΧΥ = 4432, ΣΧ? = 1910 Step 3: Use the following equations to find a and b: α – ΣΥΣΧ? - ΣΧΣΧΥ η-ΣΧ2 – (ΣΧ)? - 276 - 1910 – 114. 4432 8. 1910 – 1142 & 9.594 6 = η-ΣΧΥ – ΣΧ.ΣΥ η-ΣΧ2 – (ΣΧ) - 8. 4432 - 114- 276 8. 1910 – (114)? Ν1.748 Step 4: Substitute a and b in regression equation formula y = α + 6.1 9 9.594 + 1.748.α

y = 9.59 + 1.75 * x (round to the nearest hundredth )

(c)

Step 1: Find XY, X2 and Y2 as it was done in the table below. X Y X-Y Χ. Χ Υ.Υ 7 18 126 49 324 8 23 184 64 529 10 28 100 784 280 416 13 32 169 1024 14 37 518 196 1369 16 41 656 256 1681 20 45 900 400 676 2025 2704 26 52 1352 Step 2: Find the sum of every column to get: ΣΧ = 114, ΣΥ = 276, ΣΧ. Υ = 4432, ΣΧ? = 1910, ΣΥ? = 10440 Step 3: Use the following formula to work out the correlation coefficient. η ΣΧΥ – ΣΧ.ΣΥ Υ [n ΣΧ? - (ΣΧ)] - [ΣΥ? - (ΣΥ?) 8. 4432 – 114 - 276 γ = 8 0.9747 [8 - 1910 – 114?] - [8 - 10440 – 276?

r =0.97 (round to the nearest hundredth )

r^2= (0.9747) ^ 2

=0.9500 = 0.95   (round to the nearest hundredth )

(D)

y=60

equestion   y = 9.59 + 1.75 * x

60= 9.59 + 1.75 * x

x = 28.80571 = 29