library(tidyverse)
library(scales)data(SaratogaHouses, package="mosaicData")
houses_lm <- lm(price ~ lotSize + age + landValue +
livingArea + bedrooms + bathrooms +
waterfront,
data = SaratogaHouses)
# View summary of model 1
summary(houses_lm)
##
## Call:
## lm(formula = price ~ lotSize + age + landValue + livingArea +
## bedrooms + bathrooms + waterfront, data = SaratogaHouses)
##
## Residuals:
## Min 1Q Median 3Q Max
## -220208 -35416 -5443 27570 464320
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.399e+05 1.647e+04 8.491 < 2e-16 ***
## lotSize 7.501e+03 2.075e+03 3.615 0.000309 ***
## age -1.360e+02 5.416e+01 -2.512 0.012099 *
## landValue 9.093e-01 4.583e-02 19.841 < 2e-16 ***
## livingArea 7.518e+01 4.158e+00 18.080 < 2e-16 ***
## bedrooms -5.767e+03 2.388e+03 -2.414 0.015863 *
## bathrooms 2.455e+04 3.332e+03 7.366 2.71e-13 ***
## waterfrontNo -1.207e+05 1.560e+04 -7.738 1.70e-14 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 59370 on 1720 degrees of freedom
## Multiple R-squared: 0.6378, Adjusted R-squared: 0.6363
## F-statistic: 432.6 on 7 and 1720 DF, p-value: < 2.2e-16Interpretation
Intercept line, for example, indicates that the coefficient is significant at 0.1% signficance level (low p-values). It means that we are 99.9% confident that the interecept is true. One the other hand, The variable age has only one star. It means that we are only 95% confident that age is meaningful in explaining home prices. If a variable had no star, it would have meant that we are not confident of the reported coefficient at all. In other words, it would be highly unlikely that changes in the variable with no star is meaningful in explaining changes in the home prices.living area is 75.18. It means that an increase of one square foot of living area is associated with a home price increase of $75, holding the other variables constant. When interpreting coeffcients, make sure to check the unit of the variables in the data.living area = 0). Of coure, living area canโt be zero. Often, interpret is meaningless.hightemp, and precip.Hint: The variables are available in the RailTrail data set from the mosaicData package.
data(RailTrail, package="mosaicData")
RailTrail_lm <- lm(volume ~ hightemp + precip,
data = RailTrail)
# View summary of model 1
summary(RailTrail_lm)
##
## Call:
## lm(formula = volume ~ hightemp + precip, data = RailTrail)
##
## Residuals:
## Min 1Q Median 3Q Max
## -271.311 -56.545 5.915 48.962 296.453
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -31.5197 55.2383 -0.571 0.56973
## hightemp 6.1177 0.7941 7.704 1.97e-11 ***
## precip -153.2608 39.3071 -3.899 0.00019 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 96.68 on 87 degrees of freedom
## Multiple R-squared: 0.4377, Adjusted R-squared: 0.4247
## F-statistic: 33.85 on 2 and 87 DF, p-value: 1.334e-11hightemp statistically significant at 5%?Yes, it is significant at 5 percent becuase its T value is smaller then .05 (5%)
hightemp?number of trail users increases by more than 6 people per degree increase in farienheight. ## Q4 Is the intercept statistically significant at 5%? The Intercept is not statistically significant at 5% becuase it is larger than .05 ## Q5 Interpret the intercept? 97 people ## Q6 Interpret the reported residual standard error. The typical difference between the RailTrail and the price and the hightemp predicted by the model is 296 In other words 296 on average. ## Q7 Interpret the reported adjusted R squared. .42 ## Q8 Hide the messages, but display the code and its results on the webpage. Hint: Use message, echo and results in the chunk options. Refer to the RMarkdown Reference Guide.