Question

1. Using data from 50 workers, a researcher estimates Wage = β₀ + β₁Education + β₂Experience + β₃Age + ε, where Wage is the hourly wage rate and Education, Experience, and Age are the years of higher education, the years of experience, and the age of the worker, respectively. The regression results are shown in the following table.

	Coefficients	Standard Error	t Stat	p-Value
Intercept	7.73	3.94	1.96	0.0558
Education	1.15	0.39	2.95	0.0050
Experience	0.45	0.11	4.09	0.0002
Age	−0.03	0.09	−0.33	0.7404

a-1. Interpret the point estimate for β₁.

• As Education increases by 1 year, Wage is predicted to increase by 1.15/hour.

• As Education increases by 1 year, Wage is predicted to increase by 0.45/hour.

• As Education increases by 1 year, Wage is predicted to increase by 1.15/hour, holding Age and Experience constant.

• As Education increases by 1 year, Wage is predicted to increase by 0.45/hour, holding Age and Experience constant.

a-2. Interpret the point estimate for β₂.

• As Experience increases by 1 year, Wage is predicted to increase by 1.15/hour.

• As Experience increases by 1 year, Wage is predicted to increase by 0.45/hour.

• As Experience increases by 1 year, Wage is predicted to increase by 1.15/hour, holding Age and Education constant.

• As Experience increases by 1 year, Wage is predicted to increase by 0.45/hour, holding Age and Education constant.

b. What is the sample regression equation? (Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.)

c. Predict the hourly wage rate for a 39-year-old worker with 3 years of higher education and 2 years of experience. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

2. A horticulturist is studying the relationship between tomato plant height and fertilizer amount. Thirty tomato plants grown in similar conditions were subjected to various amounts of fertilizer (in ounces) over a four-month period, and then their heights (in inches) were measured. [You may find it useful to reference the t table.]

Fertilizer (ounces)	Height (inches)
1.9	20.8
4.0	49.4
4.1	56.7
1.3	24.4
4.4	29.2
5.1	60.3
3.2	24.5
1.0	25.7
2.4	26.1
2.4	25.7
0.9	26.7
2.0	28.7
4.3	62.3
3.3	30.9
5.1	43.1
2.6	33.5
4.0	35.1
1.4	22.5
3.6	40.1
6.0	44.1
3.3	29.1
0.7	21.2
1.4	25.8
2.6	29.2
4.4	27.7
3.7	32.3
6.0	33.7
1.0	22.7
2.6	27.1
3.2	46.1

a. Estimate: HeightˆHeight^⁢ = β₀ + β₁ Fertilizer + ε. (Round your answers to 2 decimal places.)

b-1. At the 1% significance level, determine if an ounce of fertilizer increases height by more than 3 units. First, specify the competing hypotheses.

• H₀: β₁ = 3; H_A: β₁ ≠ 3

• H₀: β₁ ≤ 3; H_A: β₁ > 3

• H₀: β₁ ≥ 3; H_A: β₁ < 3

b-2. Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)


b-3. Find the p-value.

• 0.025 p-value < 0.05
• 0.01  p-value < 0.025

• p-value < 0.01

• p-value  0.10
• 0.05  p-value < 0.10

b-4. At the 1% level of significance, what is the conclusion to the test?

Answer 1

Regression equation we have

Wage = β0+ β1Education + β2 experience + β age + ε              ....(1)

#a1) Using information given in table

We have coefficient of β0 = 7.73, β1=1.15, β2 = 0.45 , β3 = -0.03 ; putting these values in (1)

Wage = 7.73+ 1.15 *Education + 0.45* experience – 0.03 age

As we have 3 regressor variable, interpretation of point estimate β1 = 1.15

“As education increase by 1 year, wage is predicted to increase by 1.15 / hour holding age and experience constant.” This is correct answer.

If we have only 1 regressor, As education increase by 1 year, wage is predicted to increase by 1.15

#a2) β2 = 0.45

As experience is increased by 1 year work is predicted to increase by 0.45 / hour, holding age and education constant.

#b) Regression equation we have

Wage = β0+ β1Education + β2 experience + β age + ε

have coefficient of β0 = 7.73, β1=1.15, β2 = 0.45 , β3 = -0.03

So sample regression equation is

Wage = 7.73+ 1.15 *Education + 0.45* experience – 0.03 age   ....(2)

#c) Given: age =39, Education = 3, experience =2

Putting this values in equation 2,

Wage = 7.73+ 1.15 *3 + 0.45* 2 – 0.03 *39

Wage = 7.73 +3.45 +0.9 – 1.17

Wage = 10.91

Predicted the hourly wage rate = 10.91