LM Table
intercept - t-value = 2.6011
speed - t-value = 9.4643 p-value = 1.488296e-12
DF = 48
F-statisitc = 1.490232e-12 on 1 and 48 DF, p-value = 1.488296e-12
ANOVA Table
speed mean sq = 21186 F value = 89.5656 Pr(>F)=1.490232e-12
residals mean sq = 236.5417
library(ISLR)
library(tidyverse)## ── Attaching packages ───────────────────────────────────────────── tidyverse 1.3.0 ──## ✓ ggplot2 3.3.2 ✓ purrr 0.3.4
## ✓ tibble 3.0.3 ✓ dplyr 1.0.2
## ✓ tidyr 1.1.2 ✓ stringr 1.4.0
## ✓ readr 1.3.1 ✓ forcats 0.5.0## ── Conflicts ──────────────────────────────────────────────── tidyverse_conflicts() ──
## x dplyr::filter() masks stats::filter()
## x dplyr::lag() masks stats::lag()data("Carseats")A)
Sales: numerical - Unit sales (in thousands) at each location.
Price: numerical - Price company charges for car seats at each site.
Urban: factor with 2 levels - “yes” (if the store is in an urban area) and “no” (if the store is in a rural area).
US: Factor with 2 leves - “yes” (if the store is in the US) and “no” (if the store is not in the US)
B)
modB<-lm(Sales~Price+Urban+US, data = Carseats)
summary(modB)##
## Call:
## lm(formula = Sales ~ Price + Urban + US, data = Carseats)
##
## Residuals:
## Min 1Q Median 3Q Max
## -6.9206 -1.6220 -0.0564 1.5786 7.0581
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 13.043469 0.651012 20.036 < 2e-16 ***
## Price -0.054459 0.005242 -10.389 < 2e-16 ***
## UrbanYes -0.021916 0.271650 -0.081 0.936
## USYes 1.200573 0.259042 4.635 4.86e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.472 on 396 degrees of freedom
## Multiple R-squared: 0.2393, Adjusted R-squared: 0.2335
## F-statistic: 41.52 on 3 and 396 DF, p-value: < 2.2e-16C)
There is a line that starts and when Sales are 0 and has a slightly negitive slope of -.05.
When the stores are Urban then the y intercept drops slightly by -.02 but this is not significant.
When The stores are in the US then the y intercept increases by 1.2 and this is significant.
D)
Price: Y= -.0545x + 13.0435
Urban (Yes): Y= -.0545x + 12.989
US (Yes): Y= -.0545x + 14.2441
E)
Price and US are statiticly signifigant.
F)
modF <- lm(Sales~Price+US, data = Carseats)
summary(modF)##
## Call:
## lm(formula = Sales ~ Price + US, data = Carseats)
##
## Residuals:
## Min 1Q Median 3Q Max
## -6.9269 -1.6286 -0.0574 1.5766 7.0515
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 13.03079 0.63098 20.652 < 2e-16 ***
## Price -0.05448 0.00523 -10.416 < 2e-16 ***
## USYes 1.19964 0.25846 4.641 4.71e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.469 on 397 degrees of freedom
## Multiple R-squared: 0.2393, Adjusted R-squared: 0.2354
## F-statistic: 62.43 on 2 and 397 DF, p-value: < 2.2e-16G)
anova(modB)## Analysis of Variance Table
##
## Response: Sales
## Df Sum Sq Mean Sq F value Pr(>F)
## Price 1 630.03 630.03 103.0603 < 2.2e-16 ***
## Urban 1 0.10 0.10 0.0158 0.9001
## US 1 131.31 131.31 21.4802 4.86e-06 ***
## Residuals 396 2420.83 6.11
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1anova(modF)## Analysis of Variance Table
##
## Response: Sales
## Df Sum Sq Mean Sq F value Pr(>F)
## Price 1 630.03 630.03 103.319 < 2.2e-16 ***
## US 1 131.37 131.37 21.543 4.707e-06 ***
## Residuals 397 2420.87 6.10
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1The model for F fits better as its residual standard error: 6.10 compared to 6.11 for A.
H)
confint(object = modB, level = 0.95)## 2.5 % 97.5 %
## (Intercept) 11.76359670 14.32334118
## Price -0.06476419 -0.04415351
## UrbanYes -0.55597316 0.51214085
## USYes 0.69130419 1.70984121