Mathematics, 02.01.2020 23:31 silvajimena74

"select the equation of the least squares line for the data: (34.0, 1.30), (32.5, 3.25), (35.0, .65), (31.0, 6.50), (30.0, 5.85), (27.5, 8.45), (29.0, 6.50)."a. ŷ= 37.643-1.0543r b. ŷ= 1.0543x - 37.643 c. ŷ= 37.643 1.1597x d. ŷ= 41.407-1.1597x e. ŷ= -37.643 1.05433x f. none of the above

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Answer from: sammi90nicole

y=-1.055 x +37.643

And the best option would be:

a. ŷ= 37.643-1.0543x

Step-by-step explanation:

We assume that the data is this one:

x: 34.0, 32.5, 35.0, 31.0, 30.0, 27.5, 29.0

y: 1.30, 3.25, 0.65, 6.50, 5.85, 8.45, 6.50

Find the least-squares line appropriate for this data.

For this case we need to calculate the slope with the following formula:

$m=\frac{S_{xy}}{S_{xx}}$

Where:

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}$

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}$

So we can find the sums like this:

$\sum_{i=1}^n x_i = 34.0+ 32.5+ 35.0+ 31.0+ 30.0+ 27.5+ 29.0
=219$

$\sum_{i=1}^n y_i =1.3+3.25+0.65+6.5+5.85+8.45+6.5=32.5$

$\sum_{i=1}^n x^2_i = 34.0^2+ 32.5^2+ 35.0^2+ 31.0^2+ 30.0^2+ 27.5^2+ 29.0^2
=6895.5$

$\sum_{i=1}^n y^2_i =1.3^2+3.25^2+0.65^2+6.5^2+5.85^2+8.45^2+6.5^2=202.8$

$\sum_{i=1}^n x_i y_i =34*1.3 + 32.5*3.25+ 35*0.65+ 31*6.5+30*5.585 +27.5*8.45 +29*6.5=970.45$

With these we can find the sums:

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=6895.5-\frac{219^2}{7}=43.929$

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}=970.45-\frac{219*32.5}{7}=-46.336$

And the slope would be:

$m=-\frac{46.336}{43.929}=-1.055$

Nowe we can find the means for x and y like this:

$\bar x= \frac{\sum x_i}{n}=\frac{219}{7}=31.286$

$\bar y= \frac{\sum y_i}{n}=\frac{32.5}{7}=4.643$

And we can find the intercept using this:

$b=\bar y -m \bar x=4.643-(-1.055*31.286)=37.643$

So the line would be given by:

y=-1.055 x +37.643

And the best option would be:

a. ŷ= 37.643-1.0543x

Answer from: Quest

well my understanding of this question is they want you to use the y=14.1x -2.3 and put the coordinates they gave you onto the line segment of y=14.1x -2.3

step-by-step explanation:

Answer from: Quest

"it's not the heat, it's the humidity". that's a partly valid phrase you may have heard in the summer, but it's actually both. the heat index, also known as the apparent temperature, is what the temperature feels like to the human body when relative humidity is combined with the air temperature. this has important considerations for the human body's comfort. when the body gets too hot, it begins to perspire or sweat to cool itself off. if the perspiration is not able to evaporate, the body cannot regulate its temperature. evaporation is a cooling process. when perspiration is evaporated off the body, it effectively reduces the body's temperature. when the atmospheric moisture content (i.e. relative humidity) is high, the rate of perspiration from the body decreases. in other words, the human body feels warmer in humid conditions. the opposite is true when the relative humidity decreases because the rate of perspiration increases. the body actually feels cooler in arid conditions. there is direct relationship between the air temperature and relative humidity and the heat index, meaning as the air temperature and relative humidity increase (decrease), the heat index increases (decreases).

step-by-step explanation:

75% of the temperatures are below what value? how do you know? 75% of the temperatures are above w

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"select the equation of the least squares line for the data: (34.0, 1.30), (32.5, 3.25), (35.0, .65...