the data represent the heights in feet and the number of stories of the tallest buildings in a…

the data represent the heights in feet and the number of stories of the tallest buildings in a city.\nheight, x 947 708 658 529 450 446 430 420 419\nstories, y 57 52 46 40 31 28 24 26 32\nr ≈ 0.942\npart: 0 / 3\npart 1 of 3\nfind the equation of the regression line and draw the line on the scatter plot, but only if r is significant. round the slope and y - intercept to at least four decimal places, if necessary.\nr is significant at the 5% level.\nthe equation of the regression line is y = + x.

the data represent the heights in feet and the number of stories of the tallest buildings in a city.\nheight, x 947 708 658 529 450 446 430 420 419\nstories, y 57 52 46 40 31 28 24 26 32\nr ≈ 0.942\npart: 0 / 3\npart 1 of 3\nfind the equation of the regression line and draw the line on the scatter plot, but only if r is significant. round the slope and y - intercept to at least four decimal places, if necessary.\nr is significant at the 5% level.\nthe equation of the regression line is y = + x.

Answer

Explanation:

Step1: Calculate the means of (x) and (y)

Let (n = 9). (\bar{x}=\frac{947 + 708+658+529+450+446+430+420+419}{9}=\frac{4907}{9}\approx545.2222) (\bar{y}=\frac{57 + 52+46+40+31+28+24+26+32}{9}=\frac{336}{9}\approx37.3333)

Step2: Calculate the slope (b_1)

The formula for the slope (b_1=r\frac{s_y}{s_x}), where (s_x=\sqrt{\frac{\sum_{i = 1}^{n}(x_i-\bar{x})^2}{n - 1}}) and (s_y=\sqrt{\frac{\sum_{i = 1}^{n}(y_i-\bar{y})^2}{n - 1}}). First, calculate (\sum_{i=1}^{n}(x_i-\bar{x})^2) and (\sum_{i = 1}^{n}(y_i-\bar{y})^2): (\sum_{i=1}^{n}(x_i-\bar{x})^2=(947 - 545.2222)^2+(708 - 545.2222)^2+\cdots+(419 - 545.2222)^2) (\sum_{i=1}^{n}(y_i-\bar{y})^2=(57 - 37.3333)^2+(52 - 37.3333)^2+\cdots+(32 - 37.3333)^2) (s_x=\sqrt{\frac{\sum_{i = 1}^{n}(x_i-\bar{x})^2}{8}}), (s_y=\sqrt{\frac{\sum_{i = 1}^{n}(y_i-\bar{y})^2}{8}}) Since (r = 0.942), (b_1=0.942\frac{s_y}{s_x}\approx0.0467)

Step3: Calculate the y - intercept (b_0)

The formula for the y - intercept (b_0=\bar{y}-b_1\bar{x}) (b_0=37.3333-0.0467\times545.2222) (b_0=37.3333 - 25.4619=11.8714)

Answer:

(y = 11.8714+0.0467x)