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dat <- read.csv("heart.csv")
head(dat)
##   X    biking   smoking heart.disease
## 1 1 30.801246 10.896608     11.769423
## 2 2 65.129215  2.219563      2.854081
## 3 3  1.959665 17.588331     17.177803
## 4 4 44.800196  2.802559      6.816647
## 5 5 69.428454 15.974505      4.062224
## 6 6 54.403626 29.333176      9.550046
str(dat)
## 'data.frame':    498 obs. of  4 variables:
##  $ X            : int  1 2 3 4 5 6 7 8 9 10 ...
##  $ biking       : num  30.8 65.13 1.96 44.8 69.43 ...
##  $ smoking      : num  10.9 2.22 17.59 2.8 15.97 ...
##  $ heart.disease: num  11.77 2.85 17.18 6.82 4.06 ...
#independent variable: biking && smoking, dependent: the percentage of people with heart disease
model <- lm(heart.disease~biking+smoking, data=dat)
summary(model)
## 
## Call:
## lm(formula = heart.disease ~ biking + smoking, data = dat)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.1789 -0.4463  0.0362  0.4422  1.9331 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 14.984658   0.080137  186.99   <2e-16 ***
## biking      -0.200133   0.001366 -146.53   <2e-16 ***
## smoking      0.178334   0.003539   50.39   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.654 on 495 degrees of freedom
## Multiple R-squared:  0.9796, Adjusted R-squared:  0.9795 
## F-statistic: 1.19e+04 on 2 and 495 DF,  p-value: < 2.2e-16
#Since the p-value is less than 0.05, the relationship between the independent variables and the dependent variable is significant. When biking increases by 1 unit, the percentage of heart disease decreases by about 0.2 units, and when smoking increases by 1 unit, the percentage of hearing disease increases by about 0.18 units.

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