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: Create scatter - diagram

On a graph, mark the points ((1014,50)), ((935,80)), ((980,60)), ((955,135)), ((995,84)) where the (x) - axis represents the barometer reading and the (y) - axis represents the maximum wind speed.

Step3: Calculate regression line (least - squares line)

The equation of the least - squares line is (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}), (n = 5), (\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}), (\bar{y}=\frac{\sum_{i = 1}^{n}y_i}{n})

First, calculate (\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}=4879087), (\sum_{i = 1}^{5}x_iy_i=1014\times50+935\times80+980\times60+955\times135+995\times84 = 437715)

(\bar{x}=\frac{4879}{5}=975.8), (\bar{y}=\frac{409}{5}=81.8)

(b=\frac{5\times437715 - 4879\times409}{5\times4879087-(4879)^{2}}) [ \begin{align*} b&=\frac{2188575-1995511}{24395435 - 23804641}\ &=\frac{193064}{590794}\ &\approx - 0.327 \end{align*} ]

(a=81.8-(- 0.327)\times975.8=81.8 + 319.1866=400.9866)

The equation of the least - squares line is (y = 400.99-0.33x)

Then draw the line (y = 400.99-0.33x) on the scatter - diagram.

This is a manual way to find the line. In practice, graphing calculators or software like Excel, Python (using libraries like matplotlib and numpy) can be used to create the scatter - diagram and draw the least - squares line more accurately.

Answer:

To answer this question fully, one needs to create a scatter - diagram with points ((1014,50)), ((935,80)), ((980,60)), ((955,135)), ((995,84)) and draw the line (y = 400.99-0.33x) on it. The actual graph cannot be provided in this text - based format, but the steps to create it are as above.