Response:
a. As student debt rises, current investment diminishes.
b. Y= 68778.2406 - 1.9112X
For each dollar increase in college debt, the average current investments decrease by 1.9112 dollars.
c. A substantial linear correlation exists between college debt and current investment as the P-value falls below 0.1.
d. Y= $59222.2406
e. R²= 0.9818
Step-by-step breakdown:
Hello!
Data has been gathered on a random sample of 20 individuals who completed their college education five years ago. The variables under consideration are:
Y: Current investment by an individual who graduated from college five years prior.
X: Total debt of an individual upon graduating five years ago.
a)
To explore the relationship between debt and investment, creating a scatterplot with the sample data is ideal.
The scatterplot demonstrates a negative correlation, indicating that as these individuals' debt increases, their current investments decrease.
Therefore, the statement that accurately describes this is: As college debt rises, current investment decreases.
b)
The population regression equation is Y= α + βX +Ei
To develop this equation, estimates for alpha and beta are required:
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
Averages:
Y[bar]= ∑Y/n= 884971/20= 44248.55
X[bar]= ∑X/n= 256594/20= 12829.70
The estimated regression equation becomes:
Y= 68778.2406 - 1.9112X
For every dollar increase in college debt, the average current investments drop by 1.9112 dollars.
c)
To evaluate if there's a linear regression between these variables, the following null hypotheses are formulated:
H₀: β = 0
H₁: β ≠ 0
α: 0.01
Testing can be performed utilizing either a Student t-test or Snedecor's F (ANOVA)
Using t= b - β = -1.91 - 0 = -31.83
Sb 0.06
The critical area and P-value for this test is two-tailed. The P-value equals: 0.0001
Since this P-value is underneath the significance level, we reject the null hypothesis.
In the case of ANOVA, the rejection area is also one-tailed to the right, corresponding to the P-value.
The P-value remains: 0.0001
Using this method, we similarly reject the null hypothesis.
This indicates that 98.18% of the variability in current investments relates to college graduation debt within the projected regression model: Y= 68778.2406 - 1.9112X
I trust this is beneficial!
