hightemp, and precip.hightemp statistically significant at 5%?hightemp?library(tidyverse)
library(scales)
options(scipen=999) 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) 139878.80484 16472.92736 8.491 < 0.0000000000000002 ***
## lotSize 7500.79232 2075.13554 3.615 0.000309 ***
## age -136.04011 54.15794 -2.512 0.012099 *
## landValue 0.90931 0.04583 19.841 < 0.0000000000000002 ***
## livingArea 75.17866 4.15811 18.080 < 0.0000000000000002 ***
## bedrooms -5766.75988 2388.43256 -2.414 0.015863 *
## bathrooms 24547.10644 3332.26775 7.366 0.000000000000271 ***
## waterfrontNo -120726.62066 15600.82783 -7.738 0.000000000000017 ***
## ---
## 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: < 0.00000000000000022Interpretation
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")
trailusers_lm <- lm(volume ~ hightemp + precip,
data = RailTrail)
# View summary of model 1
summary(trailusers_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 0.0000000000197 ***
## 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: 0.00000000001334hightemp statistically significant at 5%?hightemp is equal to *** equaling 0.0000000000197, so yes the coefficient for hightemp is statistacally significant.
hightemp?Through the data, every time the temp goes up 1% 6 more people come to hike.
No, the Intercept is not statistically significant because the intercept is 0.56973 equaling almost 57% so its more then 5%.
The techinacal interpretation is -31.5197 but this is meaningless because you cant have -31 people.
the error is 96.68 on 87 degrees of freedom people are using the trails. It misses the line by 96.68
R squared is adjusted to 0.4247. 42% of changes in trail users are explained thtough the model.
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