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
nekit [7.7K]
3 years ago
11

The following estimated regression model was developed relating yearly income (y in $1000s) of 30 individuals with their age (x1

) and their gender (x2) (0 if male and 1 if female).
ŷ = 30 + 0.7x1 + 3x2

Also provided are SST = 1200 and SSE = 384.
The multiple coefficient of determination is _____.

a. .50
b. .42
c. .68
d. .32
Mathematics
1 answer:
ira [324]3 years ago
4 0

Answer:

R^2 = \frac{SSE}{SST}=\frac{384}{1200}=0.32

So the best option is  b. .42

Step-by-step explanation:

Previous concepts

Analysis of variance (ANOVA) "is used to analyze the differences among group means in a sample".  

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"  

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.  And is defined as:

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

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.

Solution to the problem

If we assume that we have k independent variables and we have  j=1,\dots,j individuals, we can define the following formulas of variation:  

SS_{total}=\sum_{j=1}^n (y_j-\bar y)^2  

SS_{regression}=SS_{model}=\sum_{j=1}^n (\hat y_{j}-\bar y)^2  

SS_{error}=\sum_{j=1}^n (y_{j}-\hat y_j)^2  

And we have this property  

SST=SS_{regression}+SS_{error}  

We can find SS_{regression}= SST-SS_{error}=1200-384=816

The degrees of freedom for the model on this case is given by df_{model}=df_{regression}=k=2 where k =2 represent the number of variables.

The degrees of freedom for the error on this case is given by df_{error}=N-k-1=30-2-1=27.

The determination coefficient when we conduct a multiple regression is defined as:

R^2 = \frac{SSE}{SST}=\frac{384}{1200}=0.32

So the best option is  b. .42

You might be interested in
2) Write the slope-intercept form of the equation of the line passing through the point (-5. -1) and perpendicular to
MAVERICK [17]
Sorry I just need points so I can have it on the phone later after work and I will have to go get it bruh was a day and a half day
8 0
3 years ago
Which numerical expression could represent this phrase?
Agata [3.3K]

Answer:

Step-by-step explanation:

63 divided by 9 times 10 minus 2

7 0
3 years ago
Tommy has a pet monkey. Every day, his monkey eats 4 apples in the morning. The monkey also eats two bananas for every banana th
Licemer1 [7]

Answer:

Step-by-step explanation:

Let x represent the number of bananas that Tommy eats.

Let y represent the total number of pieces of fruit that the monkey eats.

Every day, his monkey eats 4 apples in the morning. The monkey also eats two bananas for every banana that tommy eats. This means that the number of bananas that the monkey eats is 2x. The expression for the total number of fruits eaten by the monkey becomes

y = 2x + 4

4 0
3 years ago
Read 2 more answers
Select the correct answer from each drop-down menu. f(x) = x2 − 8x + 15 g(x) = x − 3 h(x) = f(x) ÷g(x) h(x) = . The domain of h(
9966 [12]

Answer:

all of them

Step-by-step explanation:

4 0
2 years ago
Read 2 more answers
Points J and K lie in plane H. Plane H contains two points. Point J is to the lower left and point K is to the uppercase right.
xxMikexx [17]

Answer:

1

Step-by-step explanation:

There's a theorem that says "through 2 points it only cross one and only one line". Having this as our start point, we can guarantee that there's only one line that can be drawn through those points

4 0
3 years ago
Read 2 more answers
Other questions:
  • What is (m+1)(m+1) multiplied
    6·1 answer
  • Edgar Anderson earns 300 a week plus a 15% commission only on sales he makes after his first 1,000 in sales. If me. Anderson’s s
    7·1 answer
  • Given the graphs of f(x) = x – 4 and g(x) = –2x – 7, what is the solution to the equation f(x) = g(x)?
    15·1 answer
  • Ashley can ride her bicycle 15 ml in 2 hours. There are 60 minutes in 1 hour and there are 1,760 in 1 mile. How many yards does
    15·1 answer
  • The product of 5 and a number x is 1 1/4<br><br> What is the value of x?
    9·1 answer
  • Which of the following are quadratic functions A. Y =5x-3/2+x^2 B. Y=x^2+5x-2 C. Y=-x+2 D. Y=x-1/x
    12·2 answers
  • If 20 buttons get me 1 dollar and i need 335 dollars how many buttons do i need?
    8·1 answer
  • Find the value of x.<br> xo<br> (x-20)<br> (2x + 10)<br> (x + 40)
    14·1 answer
  • Help pleaseeeeeeeeeeeeeeeeeee brainliest will be coming to you
    11·2 answers
  • Answer the following.
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!