Question

House Prices:

Notes on variables:

Price: In thousands of dollars

Ac: air conditioner (1 if yes, 0 if no)

Size: In square feet

Age: In years

Pool: (1 if yes, 0 if no)

Bedrms: Number of Bedrooms

Baths: Number of Bathrooms

4)   a. Make a Scatter plot where x=size and y=price

       b. Calculate the Least Squares Regression (LSR) equation:

       c. Does the intercept make sense? Why or why not?

       c. Find and interpret the R²

d. Predict the average price of a home that is 1000 square feet.

e. Better interpretation of the slope: If the square footage increased by 40 square feet, then how more would you expect the house to cost?

f. Plot the residuals vs. X-values.

g. Use the residuals plot or the regression line to identify any outliers. (If there are any.)

5) Looking at Heights again. Remember women have a mean height m= 65 in. and a standard deviation s =2.5 in. and men have a mean height of m=70 and a standard deviation s= 3

       a. What proportion of women are taller than 69 in?

b. What height for men is the 65^th percentile (larger than 65% of the data)?

c. What proportion/percentage of men have height between 68 to 75?

price ac size age pool bedrms baths 107 0 736 39 0 2 1 133 0 720 63 0 2 1 141 0 768 66 0 2 1 165 0 929 41 0 3 1 170 0 1080 44 0 3 1 173 0 942 65 0 2 1 182 0 1000 40 0 3 1 200 0 1472 66 0 3 2 220 0 1200 69 0 3 1 226 0 1302 49 0 3 2 260 1 2109 37 0 3 2 275 0 1528 41 0 2 2 280 0 1421 41 1 3 2 289 1 1753 1 0 3 2 295 0 1528 32 0 3 2 300 0 1643 29 1 3 2 310 0 1675 63 0 3 2 315 1 1714 38 0 3 2 350 0 2150 75 0 4 2 365 1 2206 28 0 4 2.5 503 1 3269 5 0 4 2.5 135 0 936 75 0 2 1 147 0 728 40 0 2 1 165 0 1014 26 0 2 1 175 1 1661 27 0 3 2 190 0 1248 42 0 3 1 191 0 1834 40 1 3 2 195 0 989 41 0 3 1 205 0 1232 43 0 2 2 210 0 1017 38 0 2 1 215 0 1216 77 0 2 1 228 0 1447 44 0 2 2 242 0 1974 65 1 4 2 250 1 1600 63 0 3 2 250 0 1168 63 1 3 1 255 0 1478 50 0 3 2 255 0 1756 36 1 3 2 265 0 1542 38 0 3 2 265 0 1633 32 1 4 2 275 1 1500 42 0 2 2 285 0 1734 62 1 3 2 365 1 1900 42 0 3 2 397 1 2468 10 0 4 2.5

Answer 1

4. Using simple R coding, we may complete the required objectives. But first, we should copy the above data to a text file (like notepad), and save it.

The R code to enter the data to a data frame would be as below.

> library(readr)

> dat <- read_delim("<location of the text file>", "\t", escape_double = FALSE, trim_ws = TRUE)

(a) The scatter plot and the required R commands would be as below.

> plot(x=dat$size,y=dat$price)

(b) The R command and regression result would be as below.

> lm(price ~ size, data = dat)

Call:
lm(formula = price ~ size, data = dat)

Coefficients:
(Intercept)         size  
    39.9621       0.1376

The regression equation would be .

The intercept represents the average price when size is zero, ie . The intercept doesn't makes sense because size of the house can not be zero.

(c) The command to find the R-squared and the resutls are as below.

> summary(lm(price ~ size, data = dat))$r.squared
[1] 0.7940702

Hence, the r-squared is 0.7940702 or 0.79 (approx).

(d) For size be 1000, we have . Hence, average price of 1000 squared feet house is $177.56.

(e) The slope is the ratio of change in average price and change in size, as . If change in size is 40, then or . Hence, for an increase in size of 40, the price rises by $5.504 or $5.5.

(f) The R command for residual plot and the plot itself would be as below.

> plot(x=dat$size,y=resid(lm(price ~ size, data = dat)))

(g) The outliers can be seen in the residual plots as datapoints for which the corresponding residuals are below -50. Except those 4 points, all the residuals lies between +50 and -50.

The corresponding datapoints can be found the the R command below.

> dat[resid(lm(price ~ size, data = dat))< -50,c(1,3)]

# A tibble: 4 x 2
  price  size
  <int> <int>
1   260  2109
2   175  1661
3   191  1834
4   242  1974

The command "resid(lm(price ~ size, data = dat))< -50" checks the residuals that are below -50, and returns TRUE if they are and false if they are not, and returns a vector of TRUE and FALSE in total. The [ , ] is used to slice the rows and columns for which the pre "," is TRUE and slices 1st and 3rd column by using the vector "c(1,3)".