Question

Find the equation of the regression line for the given data. Then construct a scatter plot of the data and draw the regression line.​ (The pair of variables have a significant​ correlation.) Then use the regression equation to predict 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 six notable buildings in a city. Height comma x 762 621 515 508 491 480 ​(a) xequals499 feet ​(b) xequals641 feet ​Stories, y 51 46 45 41 37 35 ​(c) xequals315 feet ​(d) xequals726 feet Find the regression equation. ModifyingAbove y with caretequals nothingxplusleft parenthesis nothing right parenthesis ​(Round the slope to three decimal places as needed. Round the​ y-intercept to two decimal places as​ needed.) Choose the correct graph below. A. 0 800 0 60 Height (feet) Stories A scatterplot has a horizontal axis labeled Height in feet from 0 to 800 in increments of 200 and a vertical axis labeled Stories from 0 to 60 in increments of 10. The following points are plotted: (742, 31), (601, 36), (495, 35), (488, 31), (471, 27), (460, 25). A trend line that falls from left to right passes through the points (200, 33), and (600, 30). All coordinates are approximate. B. 0 800 0 60 Height (feet) Stories A scatterplot has a horizontal axis labeled Height in feet from 0 to 800 in increments of 200 and a vertical axis labeled Stories from 0 to 60 in increments of 10. The following points are plotted: (752, 33), (601, 31), (485, 30), (458, 41), (331, 27), (280, 35). A trend line that falls from left to right passes through the points (200, 44), and (600, 40). All coordinates are approximate. C. 0 800 0 60 Height (feet) Stories A scatterplot has a horizontal axis labeled Height in feet from 0 to 800 in increments of 200 and a vertical axis labeled Stories from 0 to 60 in increments of 10. The following points are plotted: (772, 56), (631, 51), (525, 50), (518, 46), (501, 42), (490, 40). A trend line that rises from left to right passes through the points (200, 35), and (600, 54). All coordinates are approximate. D. 0 800 0 60 Height (feet) Stories A scatterplot has a horizontal axis labeled Height in feet from 0 to 800 in increments of 200 and a vertical axis labeled Stories from 0 to 60 in increments of 10. The following points are plotted: (762, 51), (621, 46), (515, 45), (508, 41), (491, 37), (480, 35). A trend line that rises from left to right passes through the points (200, 25), and (600, 44). All coordinates are approximate. ​(a) Predict the value of y for xequals499. Choose the correct answer below. A. 40 B. 51 C. 46 D. not meaningful ​(b) Predict the value of y for xequals641. Choose the correct answer below. A. 46 B. 31 C. 40 D. not meaningful ​(c) Predict the value of y for xequals315. Choose the correct answer below. A. 46 B. 51 C. 31 D. not meaningful ​(d) Predict the value of y for xequals726. Choose the correct answer below. A. 51 B. 40 C. 31 D. not meaningful

Answer 1

data

x	y
758	51
621	46
515	45
508	41
491	37
480	35

Excel

data -> data analysis -> regression

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.874732778
R Square	0.765157432
Adjusted R Square	0.70644679
Standard Error	3.246314868
Observations	6
ANOVA
	df	SS	MS	F	Significance F
Regression	1	137.3457591	137.3457591	13.03268722	0.022554977
Residual	4	42.15424089	10.53856022
Total	5	179.5
	Coefficients	Standard Error	t Stat	P-value	Lower 95%
Intercept	15.32730685	7.642678421	2.005488915	0.11539128	-5.892170242
x	0.048335653	0.013389076	3.610081331	0.022554977	0.011161619

y^= 15.3273 + 0.0483 x

x	predicted
499	39.44679789
641	46.31046068
315	NA
726	50.41899121

315 is not meaningful as 315 is not in range of sample data