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
Aliun [14]
3 years ago
11

A regression and correlation analysis resulted in the following information regarding a dependent variable (y) and an independen

t variable (x). ΣΧ=90 yY 170 n = 10 SSE 505.98 XY-Y)(X-X) = 466 2(X - X)2 234 ECY Y21434 1.1. The least squares estimate of bi equals 1.2. The least squares estimate of bo equals 1.3. The sum of squares due to regression (SSR) is 1.4. The coefficient of determination equals
Mathematics
1 answer:
Sunny_sXe [5.5K]3 years ago
4 0

Answer:

1)  \hat \beta_1 =\frac{466}{234}=1.991

2) \hat \beta_o = 18.89 -1.991 (9)=0.970

3) SSR= SST-SSE= 1434-505.98=928.02

4) r=\frac{466}{\sqrt{[234][\sum(1434]}}=0.804

And the determination coeffecient is r^2 = 0.804^2 =0.647  

Step-by-step explanation:

The correlation coefficient is a "statistical measure that calculates the strength of the relationship between the relative movements of two variables". It's denoted by r and its always between -1 and 1.  

The sum of squares "is the sum of the square of variation, where variation is defined as the spread between each individual value and the grand mean"  

When we conduct a multiple regression we want to know about the relationship between several independent or predictor variables and a dependent or criterion variable.

Data given

n=10 \sum (x-\bar x)(y-\bar y) =466,\sum (x-\bar x)^2 =234 , \sum(y-\bar y)^2 =1434  

Part 1

The slope is given by this formula:

\hat \beta_1 =\frac{\sum (x-\bar x) (y-\bar y)}{\sum (x-\bar x )^2}

If we replace we got:

\hat \beta_1 =\frac{466}{234}=1.991

Part 2

We can find the intercept with the following formula

\hat \beta_o = \bar y -\hat \beta_1 \bar x

We can find the average for x and y like this:

\bar X=90/10 = 9. \bar y= 170/9=18.89

And replacing we got:

\hat \beta_o = 18.89 -1.991 (9)=0.970

Part 3

For this case we have the SSE=505.98 who represent the sum of squares for the error.

The total sum of squares is given by SST \sum (y-\bar y)^2 = 1434

And since the total variation is the sum of squares for the regression and the error we have this:

SST= SSR+SSE

And solving for SSR we got:

SSR= SST-SSE= 1434-505.98=928.02

Part 4

In order to calculate the correlation coefficient we can use this formula:  

r=\frac{\sum (x-\bar x)(y-\bar y) }{\sqrt{[\sum (x-\bar x)^2][\sum(y-\bar y)^2]}}  

For our case we have this:  

n=10 \sum (x-\bar x)(y-\bar y) =466,\sum (x-\bar x)^2 =234 , \sum(y-\bar y)^2 =1434  

So we can find the correlation coefficient replacing like this:

r=\frac{466}{\sqrt{[234][\sum(1434]}}=0.804

And the determination coeffecient is r^2 = 0.804^2 =0.647  

You might be interested in
A clock has a face with a radius of 11.5 centimeters. What is the approximate circumference of the clock?
antiseptic1488 [7]
C = 2 pi r
C = 2 x 3.14 x 11.5
C = 72.22
answer is <span>
A. 72.22 cm</span>
6 0
2 years ago
Read 2 more answers
Please help me so stressed
mr Goodwill [35]

Answer:

Meron ka nang loptap bakit humihingi ka pa nang answer

8 0
2 years ago
HELP!!!<br> what is x?<br> x2/4*=50
Gnoma [55]
Hello there. 

THe answer is x=100.

Plz branliest
5 0
3 years ago
Read 2 more answers
How much area will the dimensions of a right triangle are 35 feet by 20 feet?
Oksana_A [137]
The area will be 700 ft.
8 0
3 years ago
Please help me! i'm begging you
lions [1.4K]
The answer for this is B
5 0
3 years ago
Read 2 more answers
Other questions:
  • Can you guys plz help me with the customary units of weight
    10·1 answer
  • Alex is saving money because she would like to purchase the new video gaming system they everyone has been talking about after 2
    11·1 answer
  • (3-7n^2+3n^3)-(6n^3-1-5n^2). Simplify.
    5·2 answers
  • The steps below show the incomplete solution to find the value of n for the equation 4n − 2n + 4 = −1 + 17:
    14·2 answers
  • What is the equation of the line in slope -intercept from that is perpendicular to the line y=3/4x-2 and passes through the poin
    7·1 answer
  • The temperature at the beginning for the day is 32°Friday and drops to -6°Friday by midnight. How many degrees did the temperatu
    8·1 answer
  • Which equation is the distance formula?
    15·1 answer
  • S(n) is a function that squares numbers. Find S(13) when S(n) =n^2
    11·1 answer
  • Complete the square to solve the equation below.
    5·1 answer
  • Five pounds of birdseed is used to fill 4 identical bird feeders. a. What fraction of the birdseed will be needed to fill each f
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!