fixing equation output

Author: leem44

regression2.Rmd

@@ -129,7 +129,7 @@ $\beta_1$ as the increase in price for each square foot of space.
 Let's push this thought even further: what would happen in the equation for the line if you 
 tried to evaluate the price of a house with size 6 *million* square feet?
 Or what about *negative* 2,000 square feet? As it turns out, nothing in the formula breaks; linear
-regression will happily make predictions for crazy predictor values if you ask it to. But even though
+regression will happily make predictions for different predictor values if you ask it to. But even though
 you *can* make these wild predictions, you shouldn't. You should only make predictions roughly within
 the range of your original data, and perhaps a bit beyond it only if it makes sense. For example,
 the data in Figure \@ref(fig:08-lin-reg1) only reaches around 800 square feet on the low end, but 
@@ -163,7 +163,7 @@ small_plot +
 
 By using simple linear regression on this small data set to predict the sale price
 for a 2,000 square-foot house, we get a predicted value of 
-\$`r format(round(prediction[[1]]), big.mark=",", nsmall=0, scientific = FALSE)`. But wait a minute...how
+\$`r format(round(prediction[[1]]), big.mark=",", nsmall=0, scientific = FALSE)`. But wait a minute... how
 exactly does simple linear regression choose the line of best fit? Many
 different lines could be drawn through the data points. 
 Some plausible examples are shown in Figure \@ref(fig:08-several-lines).
@@ -783,11 +783,11 @@ has regression coefficients that are very sensitive to the exact values in the d
 if we change the data ever so slightly—e.g., by running cross-validation, which splits
 up the data randomly into different chunks—the coefficients vary by large amounts:
 
-Best Fit 1: $\text{house sale price} = `r icept1` + `r sqft1`\cdot (\text{house size 1 (ft$^2$)}) + `r sqft11` \cdot (\text{house size 2 (ft$^2$)}).$
+Best Fit 1: $\text{house sale price} = `r icept1` + (`r sqft1`)\cdot (\text{house size 1 (ft$^2$)}) + (`r sqft11`) \cdot (\text{house size 2 (ft$^2$)}).$
 
-Best Fit 2: $\text{house sale price} = `r icept2` + `r sqft2`\cdot (\text{house size 1 (ft$^2$)}) + `r sqft22` \cdot (\text{house size 2 (ft$^2$)}).$
+Best Fit 2: $\text{house sale price} = `r icept2` + (`r sqft2`)\cdot (\text{house size 1 (ft$^2$)}) + (`r sqft22`) \cdot (\text{house size 2 (ft$^2$)}).$
 
-Best Fit 3: $\text{house sale price} = `r icept3` + `r sqft3`\cdot (\text{house size 1 (ft$^2$)}) + `r sqft33` \cdot (\text{house size 2 (ft$^2$)}).$
+Best Fit 3: $\text{house sale price} = `r icept3` + (`r sqft3`)\cdot (\text{house size 1 (ft$^2$)}) + (`r sqft33`) \cdot (\text{house size 2 (ft$^2$)}).$
 
  Therefore, when performing multivariable linear regression, it is important to avoid including very
 linearly related predictors. However, techniques for doing so are beyond the scope of this