#Exercise 1.

Revisit Exercise 1 from Homework 6. Print a list of messages describing the effect size for each unique pair of means from `CaloriesPerRecipe`. Your messages should look like

```
The difference between 1936 and 1945 is ####. This is a ???? difference.
The difference between 1936 and 1951 is ####. This is a ???? difference.
...
```

`####` should be replaced with absolute value for the difference between pair of means, and `????` will be `small`, `medium` or `large`. Calculate Cohen $d$ for each pair, and use $d<0.2$ to determine small effects and $d>0.8$ for large effects.

Print each message on a single line. The result will look better if you use `cat` in R.

If you use SAS, used `scan` to iterate over the list macro variables `CaloriesPerRecipeMean` and `CaloriesPerRecipeSD`. You can put the results to the log.

```{r}
cohen.d <- function(M_1, M_2, S_1, S_2) {
d <- abs(M_1-M_2)/sqrt((S_1**2+S_2**2)/2)
return(d)
}
len <- length(Year)
df <- data.frame()
for(i in seq(1, len-1)){
for(j in seq(i+1, len)){
if(i != j){
   r <- data.frame(Year[i], Year[j], CaloriesPerRecipeMean[j], CaloriesPerRecipeMean[i],
                  cohen.d(CaloriesPerRecipeMean[j], CaloriesPerRecipeMean[i],
   CaloriesPerRecipeSD[j], CaloriesPerRecipeSD[i]))
   df <- rbind(df, r)
}
}
}
names(df) <- c("Year1", "Year2", "Mean1", "Mean2", "CohenD")
df$diff <- abs(df$Mean1 - df$Mean2)
df$effect <- ifelse(df$CohenD < 0.2, "small", ifelse(df$CohenD > 0.8, "large", "medium"))
apply(df, 1, FUN = function(x){
cat("The difference between ", x[1], " and ", x[2], " is ", x[6],". This is a ", x[7], " difference.", sep = "")
cat("\n")
})
```

1 Suppose you the multiple regression model 60+ 63x1 62x2 + â‚¬...