Question 7. (6 points) tenure is years with current employer. Since tenure captures the productivity of the individual at a particular job, we may consider it as a determinant of hourly earnings. Regress ln(wage) on educ, exper, and tenure (3 points). Using the estimates, compute the estimated effect on wage when an individual stays at the same firm for another year (3 points). Note that when tenure increases by one year, exper must also increase by one year. Question 8.	(8 points) Is your predicted effect in Question 7 statistically significantly different from zero at the seven percent of level? Clearly write down the null hypothesis (3 points). Test your hypothesis using R by loading relevant packages (2 point). Explain your decision whether to reject the hypothesis (3 points). how to do question 8 in r

### Question 8: Testing for Statistical Significance in R

To solve Question 8, you will need to test whether the effect of **tenure** (or the combination of **tenure** and **exper** since they both increase by one year) is statistically significantly different from zero at a 7% significance level. Here are the steps and the corresponding code in R to conduct this test:

#### Step-by-Step Explanation:

1. **Null Hypothesis**:  
   You want to check if the combined effect of an additional year of tenure and experience is statistically different from zero. The null hypothesis is that the coefficient of **tenure** (or combined with **exper**) is zero. 

   \[
   H_0: \beta_{tenure} = 0
   \]

   The alternative hypothesis is:

   \[
   H_1: \beta_{tenure} \neq 0
   \]

2. **Load the necessary R packages**:  
   You will need the `lm()` function from the `stats` package for linear regression, which comes pre-installed with R. You also may use `broom` for cleaner output, though it's optional.

3. **Run the regression model**:  
   Regress `ln(wage)` on `educ`, `exper`, and `tenure` using the `lm()` function.

4. **Obtain the p-value**:  
   You can extract the p-value for the coefficient of `tenure` (which also includes the effect of `exper` since it increases simultaneously) to determine if it's statistically significant at the 7% significance level.

5. **Decision rule**:  
   If the p-value is less than 0.07 (7% significance level), you reject the null hypothesis.

#### R Code Implementation:

```r
# Load necessary packages (install broom if not already installed)
# install.packages("broom") # Uncomment if broom is not installed
library(broom)

# Assuming your data is stored in a data frame called `data`
# Example data frame: data <- data.frame(ln_wage, educ, exper, tenure)

# Perform the regression
model <- lm(ln_wage ~ educ + exper + tenure, data = data)

# Summary of the model
summary(model)

# Get the p-value for the tenure coefficient (which represents the combined effect of tenure and experience)
# Use the `broom` package for a clean output (optional)
tidy(model)

# Extract the p-value for the tenure coefficient
p_value_tenure <- tidy(model)$p.value[which(tidy(model)$term == "tenure")]

# Compare the p-value with the 7% significance level
if (p_value_tenure < 0.07) {
  print("Reject the null hypothesis: The effect of tenure is statistically significant.")
} else {
  print("Fail to reject the null hypothesis: The effect of tenure is not statistically significant.")
}
```

#### Explanation of Decision:

- After running the regression, focus on the p-value associated with the **tenure** coefficient.
- If the p-value is smaller than 0.07, this means there is evidence to suggest that **tenure** has a statistically significant effect on wages, and you should **reject the null hypothesis**.
- If the p-value is greater than 0.07, you **fail to reject the null hypothesis**, implying that the effect of **tenure** on wages is not statistically significant at the 7% significance level.

---

Would you like more details or have any questions on how to proceed?

### 5 Related Questions:
1. How do I interpret the regression coefficients in the summary output?
2. What does it mean if the p-value is very close to 0.07?
3. How do I calculate confidence intervals for the tenure effect in R?
4. Can I test for statistical significance using a different significance level?
5. How can I visualize the relationship between tenure and wage using R?

### Tip:
When performing hypothesis tests, always ensure that the assumptions of the regression model (like homoscedasticity and normality of residuals) are met to ensure valid results.

Question 7. (6 points) tenure is years with current employer. Since tenure captures the productivity of the individual at a particular job, we may consider it as a determinant of hourly earnings. Regress ln(wage) on educ, exper, and tenure (3 points). Using the estimates, compute the estimated effect on wage when an individual stays at the same firm for another year (3 points). Note that when tenure increases by one year, exper must also increase by one year. Question 8. (8 points) Is your predicted effect in Question 7 statistically significantly different from zero at the seven percent of level? Clearly write down the null hypothesis (3 points). Test your hypothesis using R by loading relevant packages (2 points). Explain your decision whether to reject the hypothesis (3 points).

Understand how to use linear regression to model the relationship between wage, education, experience, and tenure. Learn how to compute the effect of tenure on wages and test statistical significance at a 7% level using R. Ideal for students studying statistics or econometrics at the university level.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation