What is the d stand for????

In a study relating the degree of warping, in mm, of a copper plate (y) to temperature in °C (x), the following summary statisti

kipiarov [429]

Answer:

The error sum of squares is SSE=12.97

The regression sum of squares is SSR=6.430

The total sum of squares is SST=19.4

Step-by-step explanation:

Linear regression is a way "to modeling the relationship between a scalar response (or dependent variable) and one or more explanatory variables (or independent variables)".

Regression estimates are "used to describe data and to explain the relationship between one dependent variable and one or more independent variables"

The linear model is given by the following equation $Y=mx +b$ , where y is the dependent variable, x the independent variable, m the slope and b the intercept.

For this case we have the following info given:

$\sum_{i=1}^n (x_i -\bar x)^2 =98775$

$\sum_{i=1}^n (y_i -\bar y)^2 =19.4$

$\bar x =26.36$

$\bar y =0.5188$

n= 40 represent the sample size

$\sum_{i=1}^n (x_i -\bar x)(y_i -\bar y) =796.94$

The total sum of squares is given by this formula:

$SST= \sum_{i=1}^n (y_i -\bar y)^2 =19.4$

And from the formulas for a simple regression, we need to calculate the slope for the regression like this:

$m=\frac{\sum_{i=1}^n (x_i -\bar x)(y_i -\bar y)}{\sum_{i=1}^n (x_i -\bar x)^2}$

And if we replace the values given we have:

$m=\frac{796.94}{98775}=0.008068$

We have another useful equation in order to find the sum of squares for the regression, given by:

$SSR=m* \sum_{i=1}^n (x_i -\bar x)(y_i -\bar y)=0.008068*796.94=6.430$

And we know this equivalence:

$SST= SSR+SSE$

And solving for the sum of squares for the error we have:

$SSE=SST-SSR=19.4-6.430=12.97$

So then we have the final solutions:

The error sum of squares is SSE=12.97

The regression sum of squares is SSR=6.430

The total sum of squares is SST=19.4

6 0

3 years ago

Elliot's employer pays time-and-a-half for all hours worked over 40 hours per week. Elliot's regular hourly rate is $9 per hour.

musickatia [10]

E=9h+1.5(9)(h-40)

e=9h+13.5(h-40), since h=49

e=9(40)+13.5(9)

e=9(40+13.5)

e=9(53.5)

e=$481.50

4 0

3 years ago

2sin^2 2x=2<br><br> In the domain [0,2pi)<br><br> What can x equal ( in radians).

lions [1.4K]

Bear in mind that, when it comes to trigonometric functions, the location of the exponent can be a bit misleading, however recall that sin²(θ) is really [ sin( θ )]²,

$\bf 2sin^2(2x)=2\implies sin^2(2x)=\cfrac{2}{2}
\\\\\\
sin^2(2x)=1\implies [sin(2x)]^2=1\implies sin(2x)=\pm\sqrt{1}
\\\\\\
sin(2x)=\pm 1\implies sin^{-1}[sin(2x)]=sin^{-1}(\pm 1)$

$\bf \measuredangle 2x=sin^{-1}(\pm 1)\implies \measuredangle 2x=
\begin{cases}
\frac{\pi }{2}\\\\
\frac{3\pi }{2}
\end{cases}\\\\
-------------------------------\\\\
\measuredangle 2x=\cfrac{\pi }{2}\implies \measuredangle x=\cfrac{\pi }{4}\qquad \qquad \qquad \qquad \measuredangle 2x=\cfrac{3\pi }{2}\implies \measuredangle x=\cfrac{3\pi }{4}$

3 0

3 years ago

Write the points (-3,5) and (1,1) in slope-intercept form

Jobisdone [24]

Y=mx+b
m=slope
b=yint

find slope
slope between (x1,y1) and (x2,y2) is (y1-y2)/(x1-x2)

given
(-3,5) and (1,1)
slope=(5-1)/(-3-1)=4/-4=-1

y=-1x+b
find b
when x=1, then y=1
1=-1(1)+b
1=-1+b
add 1
2=b

y=-x+2

3 0

3 years ago

What is the midpointof the segment with endpoint (-3,7) and (9,5)?

PolarNik [594]

(-3,7)(9,5)

midpoint formula : (x1 + x2)/2 , (y1 + y1)/2

(-3 + 9)/2 , (7 + 5)/2 = (6/2, 12/2) = (3,6) <==

8 0

2 years ago