# Set-up Before doing anything, run this chunk: ```{ r, message=FALSE} library(tidyverse) ``` # Estimating Boston housing prices ## Data **CODE** *Start by loading the
# Set-up Before doing anything, run this chunk: ```{
r, message=FALSE} library(tidyverse) ``` # Estimating Boston housing prices ## Data **CODE** *Start by loading the data with "ast2018sample.csv" with `read.csv()`. Assign the output to an object called "df".* ```{r} # your code here ``` **CODE** *Use `dim()` to check how many rows and columns are in the data:* ```{r} # your code here ``` You will build a model of housing prices using linear regression, so first you need to check if the variable on housing prices (`AV_TOTAL`) is normally distributed. **CODE** *Use `ggplot` with `geom_density()` to plot the distribution of house prices:* ```{r} # your code here ``` **WRITING** *What do you notice about your plot?* **CODE** *Next, create a variable called "log_price" that calculates the log of house prices. Make sure you add this variable to `df`.* ```{r} # your code here ``` **CODE** *OK, now use `ggplot` with `geom_density()` to plot the distribution of *log* house prices: ```{r} # your code here ``` **WRITING** *What do you notice about your plot of the distribution of **log** prices?* ## Summarization **CODE** *Use `summarize()` to calculate average log prices:* ```{r} # your code here ``` **CODE** *Use `group_by()` and `summarize()` and `n()` to calculate the number of observations per ZIPCODE (`ZIPCODE`):* ```{r} # your code here ``` **CODE** *Use `group_by()` and `summarize()` to calculate the average and standard deviation of log prices by ZIPCODE (`ZIPCODE`):* ```{r} # your code here ``` Let's focus the rest of our analysis on the zipcode [2132](https://www.google.com/maps/place/Boston,+MA+02132/@42.2922626,-71.2432236,11.76z/data=!4m5!3m4!1s0x89e37f3c80e4b4ad:0xeef4364fd79e1466!8m2!3d42.2797554!4d-71.1626756). **CODE** *Filter out all observations that are not from the zipcode 2132 and assign the output to a new object called "df_2132":* ```{r} # your code here ``` **CODE** *Calculate the average, median and standard deviation of log price for `df_2132`:* ```{r} # your code here ``` ## Visualization (Make sure you use the data `df_2132`) **CODE** *Make of a scatterplot of log prices on the y-axis and the number of bedrooms (`R_BDRMS`) on the x-axis:* ```{r} # your code here ``` **WRITING** *What do you notice?* **CODE** *Make of a scatterplot of log prices on y-axis and the total square feet of living area (`LIVING_AREA`) on the x-axis:* ```{r} # your code here ``` **WRITING** *What do you notice?* **CODE** *Use a scatterplot to check if there is a relationship between the year a house was built (`YR_BUILT`) and its log price:* ```{r} # your code here ``` **WRITING** *What do you notice?* **CODE** *Use `stat_summary` to plot the average log price against `OWN_OCC` (a dummy variable indicating whether a property is owner-occupied):* ```{r} # your code here ``` **WRITING** *Does it look like log prices vary depending on whether a property is owner occupied?* ## Inference **CODE** *Estimate a linear model of log house prices as a function of:* * the total living area (`LIVING_AREA`) * the number of bedrooms (`R_BDRMS`) * the number of full bathrooms (`R_FULL_BTH`) * the number of half bathrooms (`R_HALF_BTH`) * whether the property is owner-occupied (`OWN_OCC`) * the number of fireplaces (`R_FPLACE`) *and assign your output to the object `m1`:* ```{r} # your code here ``` **WRITING** *Interpret the coefficient on LIVING_AREA (recall it is measured in square feet). Be sure to note whether the coefficient is significant (and if so, why):* **WRITING** *Interpret the coefficient on OWN_OCCY. Be sure to note whether the coefficient is significant (and if so, why):* # Estimating the value of air quality Load this [data on housing prices](https://deepblue.lib.umich.edu/handle/2027.42/22636) by running the chunk: ```{r} hprice2 = wooldridge::hprice2 head(hprice2) ``` The data include the following variables * `price`: median housing price. * `nox`: Nitrous Oxide (NOX) concentration; parts per million. * `crime`: number of reported crimes per capita. * `rooms`: average number of rooms in houses in the community. * `dist`: weighted distance of the community to 5 employment centers. * `stratio`: average student-teacher ratio of schools in the community. **CODE** *Make a scatterplot of prices as a function of NOX.* ```{r} # your code here ``` **WRITING** *What do you notice?* **CODE** *Make a scatterplot of prices as a function of crime.* ```{r} # your code here ``` **WRITING** *What do you notice?* **CODE** *Run a regression that estimates price as linear function of* * `nox`: [Nitrous Oxide (NOX)](https://en.wikipedia.org/wiki/Nitrous_oxide) concentration; parts per million. * `crime`: number of reported crimes per capita. * `rooms`: average number of rooms in houses in the community. * `dist`: weighted distance of the community to 5 employment centers. * `stratio`: average student-teacher ratio of schools in the community. *and save the output to the object `m2`:* ```{r} # your code here ``` **CODE** *Verify the t-value for `proptax` is equal to the estimated coefficient divided by the standard error:* ```{r} # your code here ``` **CODE** *Verify the p-value for `proptax` using `pt()` (hint: there are 499 degrees of freedom, because we have $n=506$ observations and $6+1=7$ covariates including the intercept):* ```{r} # your code here ``` **WRITING** *What does it mean for a regression coefficient to be statistically significant?* **WRITING** *What is the hypothesis test on `proptax`? (Be sure to state both the null and alternative hypotheses)* **WRITING** *What is the hypothesis test on `nox`? (Be sure to state both the null and alternative hypotheses)* **WRITING** *Interpret the coefficient on `nox` (recall it is measured in parts per million). Be sure to note whether the coefficient is significant (and if so, why):* **WRITING** *Which has a larger average effect on prices in this sample: pollution or crime?*
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Authors: Shakir Al Ghalayini, Mohammed A. Keshta, Thabet M. Hassan
1st Edition
3656943052, 978-3656943051
