Answer:
.
Step-by-step explanation:
Given : 9,540,000
To find : Write 9,540,000 in expanded form using exponents to show powers of 10.
Solution : We have given 9,540,000
Here 9 is at million place 9000000
5 is at hundred thousand place = 500,000.
4 is at tens thousand place = 40,000
We expanded it as
9, 000,000 + 500,000+40,000.
In term of power of 10.
.
Therefore,
.
Answer:
a. As college debt increases current investment decreases.
b. Y= 68778.2406 - 1.9112X
Every time the college debt increases one dollar, the estimated mean of the current investments decreases 1.9112 dollars.
c. There is a significant linear relationship between college debt and current investment because the P-value is less than 0.1.
d. Y= $59222.2406
e. R²= 0.9818
Step-by-step explanation:
Hello!
You have the information on a random sample of 20 individuals who graduated from college five years ago. The variables of interest are:
Y: Current investment of an individual that graduated from college 5 years ago.
X: Total debt of an individual when he graduated from college 5 years ago.
a)
To see the relationship between the information about the debt and the investment is it best to make a scatterplot with the sample information.
As you can see in the scatterplot (attachment) there is a negative relationship between the current investment and the debt after college, this means that the greater the debt these individuals had, the less they are currently investing.
The statement that best describes it is: As college debt increases current investment decreases.
b)
The population regression equation is Y= α + βX +Ei
To develope the regression equation you have to estimate alpha and beta:
a= Y[bar] -bX[bar]
a= 44248.55 - (-1.91)*12829.70
a= 68778.2406
b=
b=
b= -1.9112
∑X= 256594
∑X²= 4515520748
∑Y= 884971
∑Y²= 43710429303
∑XY= 9014653088
n= 20
Means:
Y[bar]= ∑Y/n= 884971/20= 44248.55
X[bar]= ∑X/n= 256594/20= 12829.70
The estimated regression equation is:
Y= 68778.2406 - 1.9112X
Every time the college debt increases one dollar, the estimated mean of the current investments decreases 1.9112 dollars.
c)
The hypotheses to test if there is a linear regression between the two variables are two tailed:
H₀: β = 0
H₁: β ≠ 0
α: 0.01
To make this test you can use either a Student t or the Snedecor's F (ANOVA)
Using t=<u> b - β </u>=<u> -1.91 - 0 </u>= -31.83
Sb 0.06
The critical region and the p-value for this test are two tailed.
The p-value is: 0.0001
The p-value is less than the level of signification, the decision is to reject the null hypothesis.
Using the
The rejection region using the ANOVA is one-tailed to the right, and so is the p-value.
The p-value is: 0.0001
Using this approach, the decision is also to reject the null hypothesis.
The conclusion is that at a 1% significance level, there is a linear regression between the current investment and the college debt.
The correct statement is:
There is a significant linear relationship between college debt and current investment because the P-value is less than 0.1.
d)
To predict what value will take Y to a given value of X you have to replace it in the estimated regression equation.
Y/X=$5000
Y= 68778.2406 - 1.9112*5000
Y= $59222.2406
The current investment of an individual that had a $5000 college debt is $59222.2406.
e)
To estimate the proportion of variation of the dependent variable that is explained/ given by the independent variable you have to calculate the coefficient of determination R².
R²= 0.9818
This means that 98.18% of the variability of the current investments are explained by the college debt at graduation under the estimated regression model: Y= 68778.2406 - 1.9112X
I hope it helps!
Cost of lectures = $7.33 per hour
<h2>Explanation</h2>Let the cost of the exam hours
Let be the cost of the workshop hours
Let be the cost of the lecture hours.
We know from our problem that exam hours cost twice as much as workshop, so:
equation (1)
We also know that workshop hours cost twice as much as lecture hours, so:
equation (2)
Finally, we also know that 3hr exams 24hr workshops and 12hr lectures cost $528, so:
equation (1)
Now, lets find the value of :
Step 1. Solve for in equation (3)
equation (4)
Step 2. Replace equation (1) in equation (4) and simplify
equation (5)
Step 3. Replace equation (2) in equation (5) and solve for
Cost of lectures = $7.33 per hour