The data below is a random sample of 3 observations drawn from the United States population. Use the data to answer the following questions:

i. Find 95% confidence intervals of the population mean of experience and wage.
ii. Estimate rhoe, w, the correlation between the variables experience and wage.
iii. Find βˆ 1 and βˆ 0, the estimates of the parameters in the following regression equation wage = β0 + β1education + ϵiv. Predict wages for a person with 15 years of education using your regression estimate. v. Find the R2wage education16.20 1212.36 1314.40 1212.00 12

Step-by-step explanation:

Hello!

You have the data for 4 observations of randomly selected employees of the U.S.  

Wage: 16.20; 12.36; 14.40; 12.00

Education: 12; 13; 12; 12

X₁: Wage of a U.S. employee.

X₂: Education of a U.S. employee.

i.

You have to estimate with a 95% confidence the population mean of each variable. Assuming all conditions are met, I'll use a students t to estimate both means.

* The general formula for the CI is: [X[bar]±*]

For population 1 (Wages)

n₁= 4; X[bar]₁= 13.74; S₁= 1.95

13.74±3.182*]

[10.65; 16.85]

Using a 95% confidence level you'd expect that the interval [10.65; 16.85] contains the population mean of the wages of U.S. employees.

For population 2 (Education)

n₂=  4; X[bar]₂= 12.25; S₂= 0.50

12.25±3.182*]

[14.45; 13.05]

Using a 95% confidence level you'd expect that the interval [14.45; 13.05] contains the value of the average education of U.S. employees.

ii.

To estimate Rho (the population correlation coefficient) you have to use the following formula:

∑X₁= 54.96; ∑X₁²= 766.57; ∑X₂= 49; ∑X₂²= 601; ∑X₁X₂= 671.88

r= -0.47

iii.

To estimate the regression using Y: wage and X: education you have to estimate the intercept and the slope of the equation:

Estimate of the slope "b"

Estimate of the intercept "a"

The estimated regression equation is ^Y= 36.28 - 1.84X

iv.

You have to estimate the value of the wages ^Y given X= 15years of education. To do so you have to replace the value of X in the estimated regression equation:

^Y= 36.28 - 1.84*15= 8.68

For a level of education of 15 years, the estimated wage is 8.68

v. The value of the coefficient of determination is R²= 0.22

This means that 22% of the variability of the average wages of U.S. employees is explained by the years of education. For the estimated model ^Y= 36.28 - 1.84X.

I hope this helps!

in mathematics, a function is a relationship between two variables such that the value of one of the variables, called the dependent variable, is determined by the value of the other variable, called the independent variable. there is a specific term we use to describe the set of independent variables of a function.

answer: the answer is 5/22

step-by-step explanation: if you subtract 17 from 22 the answer is 5 therefore the remainder of students are female