#1
snow<-read.delim2("clipboard")
summary(snow)

lm.1<-lm(diam~temp, data=snow)# fitting the model
anova(lm.1)
# Analysis of Variance Table
# 
# Response: diam
#           Df Sum Sq Mean Sq F value    Pr(>F)    
# temp       1 32.798  32.798  89.111 6.652e-07 ***
# Residuals 12  4.417   0.368                      
# ---
# Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

plot(lm.1) # Regression diagnostics plots

summary(lm.1)# Summary of the model and regression coefficients
# Call:
# lm(formula = diam ~ temp, data = snow)
# 
# Residuals:
#      Min       1Q   Median       3Q      Max 
# -1.05721 -0.21684  0.07169  0.17846  1.12766 
# 
# Coefficients:
#             Estimate Std. Error t value Pr(>|t|)    
# (Intercept) 10.65537    0.31037   34.33 2.37e-13 ***
# temp         0.26101    0.02765    9.44 6.65e-07 ***
# ---
# Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
# 
# Residual standard error: 0.6067 on 12 degrees of freedom
# Multiple R-squared:  0.8813,	Adjusted R-squared:  0.8714 
# F-statistic: 89.11 on 1 and 12 DF,  p-value: 6.652e-07

library(ggplot2)
#Plotting the scatterplot with regression line
ggplot(snow, aes(x=temp, y=diam))+geom_point()+
  geom_smooth(method="lm", col=1)+theme_classic()


predict(lm.1, newdata=data.frame(temp=-15)) # Prediction from the
# regression for a new value of the predictor

predict(lm.1, newdata=data.frame(temp=5)) # Beware of extrapolation!

#2
beer<-read.delim2("clipboard")
summary(beer)
cor.test(beer$beer, beer$IQ)
# 	Pearson's product-moment correlation
# 
# data:  beer$beer and beer$IQ
# t = -0.51757, df = 10, p-value = 0.616
# alternative hypothesis: true correlation is not equal to 0
# 95 percent confidence interval:
#  -0.6730350  0.4545116
# sample estimates:
#        cor 
# -0.1615223 

summary(lm(beer$beer~beer$IQ))# The lm gives the same result as Pearson correlation
# Call:
# lm(formula = beer$beer ~ beer$IQ)
# 
# Residuals:
#     Min      1Q  Median      3Q     Max 
# -2.4630 -1.7059 -1.1746  0.6413  5.5177 
# 
# Coefficients:
#             Estimate Std. Error t value Pr(>|t|)
# (Intercept)  5.56435    4.95234   1.124    0.287
# beer$IQ     -0.02802    0.05413  -0.518    0.616
# 
# Residual standard error: 2.71 on 10 degrees of freedom
# Multiple R-squared:  0.02609,	Adjusted R-squared:  -0.0713 
# F-statistic: 0.2679 on 1 and 10 DF,  p-value: 0.616

# The scatterplot should not contain any regression line if not significant.
ggplot(beer, aes(x=beer, y=IQ))+geom_point()+theme_classic()