can a low barometer reading be used to predict maximum wind spe be the maximum wind speed (in miles per…

Explanation:

Step1: Prepare data points

We have data points ((x_1,y_1)=(1014,50)), ((x_2,y_2)=(935,80)), ((x_3,y_3)=(980,60)), ((x_4,y_4)=(955,135)), ((x_5,y_5)=(995,84))

Step2: Plot scatter - diagram

On a graph with (x) - axis representing barometer reading and (y) - axis representing maximum wind speed, plot the above - mentioned points.

Step3: Calculate regression line

The equation of the least - squares regression line is (\hat{y}=a + bx), where (b=\frac{n\sum_{i = 1}^{n}x_iy_i-\sum_{i = 1}^{n}x_i\sum_{i = 1}^{n}y_i}{n\sum_{i = 1}^{n}x_i^{2}-(\sum_{i = 1}^{n}x_i)^{2}}) and (a=\bar{y}-b\bar{x})

First, calculate the necessary sums: (n = 5) (\sum_{i=1}^{5}x_i=1014 + 935+980+955+995=4879) (\sum_{i=1}^{5}y_i=50 + 80+60+135+84=409) (\sum_{i=1}^{5}x_i^{2}=1014^{2}+935^{2}+980^{2}+955^{2}+995^{2}) (=1028196+874225+960400+912025+990025 = 4764871) (\sum_{i=1}^{5}x_iy_i=1014\times50+935\times80+980\times60+955\times135+995\times84) (=50700+74800+58800+129925+83580=397805)

(b=\frac{5\times397805 - 4879\times409}{5\times4764871-(4879)^{2}}) (=\frac{1989025-1995511}{23824355 - 23804641}=\frac{- 6486}{19714}\approx - 0.33)

(\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}=\frac{4879}{5}=975.8) (\bar{y}=\frac{\sum_{i = 1}^{n}y_i}{n}=\frac{409}{5}=81.8)

(a=81.8-(- 0.33)\times975.8=81.8 + 322.014=403.814)

The regression line is (\hat{y}=403.814-0.33x)

Draw this line on the scatter - diagram.

Answer:

The scatter - diagram has been plotted with the points ((1014,50)), ((935,80)), ((980,60)), ((955,135)), ((995,84)) and the regression line (\hat{y}=403.814 - 0.33x) has been drawn on it.