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3 years ago

Best explained and correct answer gets brainliest.

Mathematics

1 answer:

ELEN [110]3 years ago

8 0

3275 = x * (1+0.075/12)^(12*10)

3275 = x * (2.11206463)

x= 3275/2.11206463 = 1550.6154

x=1550.62

she needs to deposit $1,550.62

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

Sunny_sXe [5.5K]

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 $r^2 = 0.804^2 =0.647$

4 0

4 years ago

The force f of an object is calculated by multiplying its mass m with acceleration a. Rearrange the formula f = ma to make mass

Katen [24]

The answer is: m=f/a. use reverse operations so that m is now the subject

7 0

3 years ago

it takes Karen 2 hours to bake 2 cakes and it takes Mark 5 hours to bake 3 cakes. If they work together how long will it take fo

Rus_ich [418]

It will take them 4 hours to bake 8 cakes

5 0

3 years ago

Student Produced Response - Calculator

faltersainse [42]

Answer:

$\dfrac{a}{b}=0.75$ .

Step-by-step explanation:

If two equations $a_1x+b_1y+c_1=0$ and $a_2x+b_2y+c_2=0$ has infinitely many solutions, then

$\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}=\dfrac{c_1}{c_2}$

The given equations are

$ax+by=10$

$3x+4y=20$

It is given that the above system of equations has infinitely many solutions. So,

$\dfrac{a}{3}=\dfrac{b}{4}=\dfrac{10}{20}$

$\dfrac{a}{3}=\dfrac{b}{4}=\dfrac{1}{2}$

Now,

$\dfrac{a}{3}=\dfrac{1}{2}$ and $\dfrac{b}{4}=\dfrac{1}{2}$

$a=\dfrac{3}{2}$ and $b=\dfrac{4}{2}$

$a=1.5$ and $b=2$

So, a=1.5 and b=2.

Now,

$\dfrac{a}{b}=\dfrac{1.5}{2}=0.75$

Therefore, $\dfrac{a}{b}=0.75$ .

5 0

4 years ago

12 +3/2s - 1/2 - 3/4s = 5/4s<br><br> How to solve for s?

rodikova [14]

s=1/23

given equation in term of s is 12+3/2s-1/2-3/4s=5/4s

to solve this first we need to take LCM on left hand side and right hand side we can rewrite given equation as 12/1+3/2s-1/2-3/4s=5/4s now taking LCM of {1,2s,2,4s,4s} is 4s then the equation becomes 48s/4s+6/4s-2s/4s-3/4s=5/4s

(48s+6-2s-3) /4s=5/4s now cancel out denominator of both side we get 48s+6-2s-3=5 this implies 46s+3=5

46s=2

s=1/23

Hence the value of s is 1/23

learn more about LCM here brainly.com/question/8463488

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3 0

2 years ago