Question

Find the equation of the regression line for the given data Then construct a cate plot of the data and draw the regressionline(The pair of variables have a significant correlation) Then use the regression equation to pred the value of y for each of the given x-values, if meaningful The table below shows the heights in feet) and the number of stories of she notable buildings in a city Height, 766 620 508 (a)x562 fost (h) x646 feet Stories, y 51 46 45 37 36 (C) x 315 feet (d) x 726 feet Find the regression equation 9- CD (Round the slope to three decimal places as needed Round the intercept to two decimal places as needed) Choose the correct graph below OA OB Ос. OD 60 Het Click to select your answer(s).

Answer 1

Solution :

Given that, Height x as 766,620,520,508,494,484

Stories y as 51,46,45,43,37,36

=> The regression equation is y^ = 0.044*x + 17.91

Explanation: We will find an equation of the regression line in 4 steps. Step 1: Find X Y and Y2 as it was done in the table below. X XY 39066 Χ Χ 586756 766 51 620 46 28520 520 45 23400 508 43 21844 384 400 270400 258064 244036 234256 494 37 18278 484 36 17424 Step 2: Find the sum of every column: ΣΧ = 3392 , ΣΥ = 258, ΣΧΥ = 148632, ΣΧ2 = 1977912 Step 3: Use the following equations to find a and b: 17.912 ΣΥΣΧ2 –ΣΧ·ΣΧΥ 258 - 1977912 – 2392 148532 ΣΧ2 - (Σκ)? 6- 1977912 – 33922 5- ΣΧΥ-ΣΧ.ΣΥ 6 · 148532 - 3392 258 8 0.044 ΣΧ2 – (ΣΧ32 6 - 1977912 – (339252 Step 4: Substitute a and b in regression equation formula και = α + 5. 17.912 + 0.044 : 0

=> Option C. graph

(a)
=> when x = 502 feet

=> The best predicted value of y for x = 502 feet is

y^(502) = 0.044*502 + 17.91

= 39.998

(b)
=> when x = 646 feet

=> The best predicted value of y for x = 646 feet is

y^(646) = 0.044*646 + 17.91

= 46.334

(c)
=> when x = 315 feet

=> The best predicted value of y for x = 315 feet is

y^(315) = 0.044*315 + 17.91

= 31.770

(d)
=> when x = 726 feet

=> The best predicted value of y for x = 726 feet is

y^(726) = 0.044*726 + 17.91

= 49.854