1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Morgarella [4.7K]
3 years ago
8

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

cs were calculated: n=40, x¯=26.36, y¯=0.5188,∑ni=1(xi−x¯)2=98,775, ∑ni=1(yi−y¯)2=19.4,∑ni=1(xi−x¯)(yi−y¯)=796.94. Compute the error sum of squares, the regression sum of squares, and the total sum of squares. Round the error sum of squares and regression sum of squares to three decimal places.
The error sum of squares is ______

The regression sum of squares is ______

The total sum of squares is _______
Mathematics
1 answer:
kipiarov [429]3 years ago
6 0

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

You might be interested in
The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells small radios. More than
Lyrx [107]
ANSWER

The company must produce and sell more than 700 radios to have a profit.

EXPLANATION

The revenue function is

R(x)=40x
and the cost function is

C(x)=5,600+32x


The company will break even when total revenue is equal to the total cost.


This implies that,


40x =5,600+32x

We group similar terms to get,


40x - 32x = 5600

This simplifies to,

8x = 5600

Divide both sides by 8 to get,


x =  \frac{5600}{8}


x = 700


The company breaks even by producing and selling 700 radios.

The company must produce and sell more than 700 radios to have a profit.
5 0
2 years ago
If anyone is good at math and likes to help someone that is not good with it I will give you brainliest
hammer [34]

Answer:

1st pic answer:

Slope= -3

Parallel slope= -3

Perpendicular slope = 1/3

2nd pic answers:

1 and 2 are parallel

1 and 3 are perpendicular

2 and 3 are perpendicular

Step-by-step explanation:

To find the slope in your first equation (6x+2y=1) you need to get y alone so that your equation will be in slope-intercept form (y=mx+b).

6x+2y=1     Start by subtracting the 6x over to the other side.

-6x      -6x

2y= -6x+1   Next divide by 2 to get y completely alone.

\frac{2y}{2} =\frac{-6x}{2}+\frac{1}{2}

y= -3x+1/2

So to answer the first part your slope is -3. Parallel slope would be the same as your regular slope. Perpendicular would be the opposite, so that means you have to flip it and change the sign.

-3 flipped is -1/3

if you change the sign it becomes positive giving you 1/3

Part 2

Your first step would be to get all the equations into the slope-intercept form (y=mx+b). The second one is already in the form so we only need to change 1 and 3.

3y=5x+2   To get y alone you need to divide everything by 3.

\frac{3y}{3}=\frac{5x}{3} +\frac{2}{3}

y=5/3x+2/3  Before we work on equation 3 we can go ahead and compare equations 1 and 2.

1: y=\frac{5x}{3} +\frac{2}{3}

2: y=\frac{5x}{3} +7   Since 1 and 2 have the same slope they would be parallel.

Now to change equation 3.

6x+10y=8    Start by subtracting the 6x over to the other side.

-6x       -6x

10y=-6x+8     Now divide everything by 10 to get y alone.

\frac{10y}{10}=\frac{-6x}{10} +\frac{8}{10}

y=-6x/10+8/10   Now we need to simplify the fractions using common factors. I'm going to use 2 for both equations, so you take -6 and 10 both divided by 2, which gives you -3 and 5(-3x/5). Now do the same with the other fraction. 8 and 10 divided by 2 gives us 4 and 5 (4/5)

3: y=\frac{-3x}{5}+\frac{4}{5}

2: y=\frac{5x}{3} +7

1: y=\frac{5x}{3} +\frac{2}{3}

Since three has an opposite slope of both 1 and 2 it would be perpendicular to both.

5 0
3 years ago
5×70=5×_ tens<br>=___tens=___.
DENIUS [597]
<span>5×70=5× 7 tens
=35 tens =350
---------------------</span>
4 0
2 years ago
Read 2 more answers
I just need the answer no explanation
SOVA2 [1]

Answer:

ok no explanation.

2 is the answer

4 0
3 years ago
Read 2 more answers
What is /-3/*-6?<br><br> When you answer could you please explain to me why the answer is that?
jekas [21]
|-3|=3 right?
Then it is
3*-6=-18
8 0
3 years ago
Other questions:
  • Drag each equation to show if it could be a correct first step to solving the equation 
    5·1 answer
  • Solve the equation with substitution 3x-2y=9 Y=2x-7
    8·1 answer
  • Solve for c: 6/15=2/c
    10·1 answer
  • Boris is taking a quiz for an online class. For the quiz, the system randomly assigns 2 high-difficulty questions, 7 moderate-di
    10·1 answer
  • Harriet works at the Mint, where new coins are made. Old and fake coins are also destroyed there. Harriet has 10 bags of $1 coin
    12·1 answer
  • Plz help me the question is in the picture below
    13·1 answer
  • ABC for life needs
    7·1 answer
  • How many millimeters are there in 4.72 meters?
    9·1 answer
  • Paul is adding mulch along the edge of his driveway. He orders 7 bags of mulch for $392. How much would it cost if Paul orders 9
    10·2 answers
  • Mrs. Silva is taking her family to Arctic Dome ice rink. The employee she spoke to on the phone said the total cost for all 5 of
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!