#$$$$$$$$$$$$$$$$$$$$$   EXE 3.1  $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#

#################################################
################## plot line ####################
#################################################
# first calculate the coefficients (beta, intercept)
# for the model where the dependent variable horsepower (hp)
# is related to the independent variable miles per gallon (mpg)
# from dataset mtcars



# plot the two variables
# add the line based on the estimates that you calculated
# above 



#################################################
################## assess fit ###################
#################################################
# calculate the fit of the model above
# check with 'lm' function
# look up function ?lm


# calculate R2 



#$$$$$$$$$$$$$$$$$$$$$   EXE 3.2  $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#

#################################################
################## dummy vars ###################
#################################################
# dummy variables have two levels like gender
# to test differences between men and women
# in an interval variable you can use a linear
# model or a t-test.

# in this exercise you will do both to see 
# how these solutions are comparable.
# try to interpret the coefficients as
# discussed during the lecture.

# use dataset juul (see last lecture)
# conduct first linear regression to
# explain igf1 (insuline growth factor) by sex


# then compare with t.test
# use var.equal=TRUE

# calculate the t-value by hand
# use var / sd and nrow / length function


# check your solution with t.test


# do the same for the independent student's t-test


#################################################
################## interval var #################
#################################################
# relate age to igf1 (both interval variables)
# plot the variables
# add the regression line
# what do you see?


##############################################################
################### t-test function ##########################
##############################################################
# for those who want to practice functions:

# to calculate the t-test, you need the 
# means and standard deviations, and observed N
# use vectorized commands (work with vectors instead 
# of looping over i)

# create function to conduct t-test on one variable
# group should be variable with 2 levels (1,2)
# use complete names, i.e. including the dataframe
ttest<-function(variable, group){
  
  # 1. create groups
  
  
  # 2. exclude missings
  
  
  # 3. calculate p value
  
  
  # 4. return values
  
}
ttest(... , ...)


# check with t.test function