The given dataset was computed from a sample of 67,248 New Hampshire residents at the age of 25-65. The sample data was obtained from the U.S. Census, 2012-2016 ACS PUMS DATA.

Q1. Describe the Grafton and Coos Counties using ALL variables in the data set.

This is an observation for Grafton and Coos countries 18.52291 =ed_avg which is the average years of schooling of New Hampshire residents in 2012-2016. 30000is the income_median which is the is the median income of New Hampshire residents in 2012-2016. It represents a total income including wages and salaries, self-employment income, and interest, dividends and rent income. resion =0 which is the place within New Hampshire: southeastern regions take 1, and 0 otherwise.

Q2. Create a scatterplot to examine the relationship between ed_avg and income_median.

Q3. Compute the correlation coefficient between the two variables and interpret them.

Hint: Make sure to interpret the direction and the magnitude of the relationship. In addition, keep in mind that correlation (or regression) coefficients do not show causation but only association.

## [1] 0.8622811

There is a strong, positive correlation between ed_avg and the income_median. This can indicate that having average eduation can result in median income.

Q4. Build a regression model to predict income_median using ed_avg, save the regression result in mod_1, and show the summary result.

## 
## Call:
## lm(formula = income_median ~ ed_avg, data = residents_25to65)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3643.9 -2548.6   655.8  1730.7  4150.6 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)   
## (Intercept)  -201503      49675  -4.056  0.00365 **
## ed_avg         12695       2636   4.816  0.00133 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2891 on 8 degrees of freedom
## Multiple R-squared:  0.7435, Adjusted R-squared:  0.7115 
## F-statistic: 23.19 on 1 and 8 DF,  p-value: 0.001328

Q5. Is the coefficient of ed_avg statistically significant at 5%? How do you know?

Hint: Discuss your answer in terms of the number of stars in the summary result. Refer to the interpretation section in quiz4_a.

** at the end of the Intercept line indicates that the coefficient is significant at 0.1% signficance level . It means that we are 99.9% confident that the interecept is true.it is signifinant at .1 percent means it is signifiant at 1% it is signifiant at 5%

Q6. Further develop the regression model above by adding another variable, region, save the regression result in mod_2, and show the summary result.

## 
## Call:
## lm(formula = income_median ~ ed_avg + region, data = residents_25to65)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2016.2  -778.4  -373.5   353.4  2780.7 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  -166192      30700  -5.413 0.000994 ***
## ed_avg         10701       1638   6.532 0.000324 ***
## region          4524       1136   3.981 0.005314 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1711 on 7 degrees of freedom
## Multiple R-squared:  0.9214, Adjusted R-squared:  0.899 
## F-statistic: 41.05 on 2 and 7 DF,  p-value: 0.0001359

Q7. Compare mod_1 and mod_2. Which of the two models better fits the data?

Hint: Discuss your answer by comparing the residual standard error and the adjusted R squared between the two models.

Model 2 fits the data better, given the residual standard error is slightly lower and the r-squared value is slightly higher. This indicates a slightly stronger predictor.

Q8. How much median income does the second model predict for the Grafton and Coos Counties?

Hint: Note that the second model has two predictors. Use both predictors to compute the predicted income.

income=y intercept + coefficent

166192+1070150=701242+166192=867434 166192+4524 50=392392+166192=558584

Q9. According to the result of the second regression model, are residents of southeastern regions of the State likely to make more income? Why or why not?

Hint: Discuss your answer based on the coefficient of region. You may refer to the interpretation section in quiz4_a.

The residents of the southeastern region are likely to make less income The intercept is 166192 means that the resion 4524 median income added with 166192=558584.

Q10.a. Hide the code but display the results of the code on the webpage.

Q10.b. Display the title and your name correctly at the top of the webpage.

Q10.c. Use the correct slug.