Question

. The height (sidewalk to roof) of notable tall buildings in America is compared to the number of stories of the building (beginning at street level).

Height (in feet)	Stories
1,050	57
428	28
362	26
529	40
790	60
401	22
380	38
1,454	110
1,127	100
700	46

a. Using “stories” as the independent variable and “height” as the dependent variable, make a scatter plot of the data.

b. Does it appear from inspection that there is a relationship between the variables?

c. Using Sum of Squares - Calculate the least squares line. Put the equation in the form of: ŷ = a + bx. Please show all your work.

d. Interpret the least square line obtained in part c.

e. Find the estimated heights for 32 stories and for 94 stories.

f. Find the correlation coefficient. Is it significant?

g. Find the Coefficient of Determination. Interpret your results.

h. Are there any outliers in the data? If so, which point(s)?

Answer 1

a.

Y Values X Values

b. Here we see that there is increasing trend, so there is positive correlation between x and y.

c.

X-M₂ Y.My 4.3 -24.7 -26.7 - 12.7 7.3 -30.7 327.9 -294.1 - 360.1 -193.1 67.9 -321.1 -342.1 731.9 404.9 -22.1 (X-Mx)2 18.49 610.09 712.89 161.29 53.29 942.49 (X-MX/Y - M) 1409.97 7264.27 9614.67 2452.37 495.67 9857.77 5028.87 41937.87 19151.77 148.07 57.3 47.3 -6.7 3283.29 2237.29 44.89 SS: 8280.1 SP: 97361.3

Sum of X = 527
Sum of Y = 7221
Mean X = 52.7
Mean Y = 722.1
Sum of squares (SSX) = 8280.1
Sum of products (SP) = 97361.3

Regression Equation = ŷ = bX + a

b = SP/SSX = 97361.3/8280.1 = 11.758

a = MY - bMX = 722.1 - (11.76*52.7) = 102.429

ŷ = 11.758X + 102.429

d. For every increase in x, there is corresponding 11.758 increase in y.

e. For x=32, ŷ = (11.758*32)+ 102.429=478.685

For x=94, ŷ = (11.758*94)+ 102.429=1207.681