Fixed typos

Exploratory_Data_Analysis/GGPlot2_Part1/lesson

@@ -99,7 +99,7 @@
   Hint: Type myhigh at the command prompt.
 
 - Class: text
-  Output: Comparing the values of myhigh with the plot, we see the first entries in the vector (29, 29, 31, 30,...) correspond to the leftmost points in the the plot (in order), and the last entries in myhigh (28, 29, 26, 26, 26) correspond to the rightmost plotted points. So, specifying the y parameter only, without an x argument, plots the values of the y argument in the order in which they occur in the data.
+  Output: Comparing the values of myhigh with the plot, we see the first entries in the vector (29, 29, 31, 30,...) correspond to the leftmost points in the plot (in order), and the last entries in myhigh (28, 29, 26, 26, 26) correspond to the rightmost plotted points. So, specifying the y parameter only, without an x argument, plots the values of the y argument in the order in which they occur in the data.
 
 - Class: cmd_question
   Output: The all-purpose qplot can also create box and whisker plots.  Call qplot now with 4 arguments. First specify the variable by which you'll split the data, in this case drv, then specify the variable which you want to examine, in this case hwy. The third argument is data (set equal to mpg), and the fourth, the geom, set equal to the string "boxplot"

R_Programming/Functions/scripts/telegram-correct.R

@@ -22,7 +22,7 @@
 # }
 #
 # The simon_says function works just like the paste function, except the
-# begining of every string is prepended by the string "Simon says:"
+# beginning of every string is prepended by the string "Simon says:"
 #
 # Telegrams used to be peppered with the words START and STOP in order to
 # demarcate the beginning and end of sentences. Write a function below called 

R_Programming/Functions/scripts/telegram.R

@@ -22,7 +22,7 @@
 # }
 #
 # The simon_says function works just like the paste function, except the
-# begining of every string is prepended by the string "Simon says:"
+# beginning of every string is prepended by the string "Simon says:"
 #
 # Telegrams used to be peppered with the words START and STOP in order to
 # demarcate the beginning and end of sentences. Write a function below called 

R_Programming_Alt/Functions/scripts/telegram-correct.R

@@ -22,7 +22,7 @@
 # }
 #
 # The simon_says function works just like the paste function, except the
-# begining of every string is prepended by the string "Simon says:"
+# beginning of every string is prepended by the string "Simon says:"
 #
 # Telegrams used to be peppered with the words START and STOP in order to
 # demarcate the beginning and end of sentences. Write a function below called 

R_Programming_Alt/Functions/scripts/telegram.R

@@ -22,7 +22,7 @@
 # }
 #
 # The simon_says function works just like the paste function, except the
-# begining of every string is prepended by the string "Simon says:"
+# beginning of every string is prepended by the string "Simon says:"
 #
 # Telegrams used to be peppered with the words START and STOP in order to
 # demarcate the beginning and end of sentences. Write a function below called 

R_Programming_Alt/Looking_at_Data/lesson.yaml

@@ -70,7 +70,7 @@
   Hint: head(plants) will show you the very top of the dataset.
 
 - Class: text
-  Output: Take a minute to look through and understand the the output above. Each row is labeled with the observation number and each column with the variable name. Your screen is probably not wide enough to view all 10 columns side-by-side, in which case R displays as many columns as it can on each line before continuing on the next.
+  Output: Take a minute to look through and understand the output above. Each row is labeled with the observation number and each column with the variable name. Your screen is probably not wide enough to view all 10 columns side-by-side, in which case R displays as many columns as it can on each line before continuing on the next.
 
 - Class: cmd_question
   Output: By default, head() shows you the first six rows of the data. You can alter this behavior by passing as a second argument the number of rows you'd like to view. Use head() to preview the first 10 rows of plants.

Regression_Models/Count_Outcomes/lesson.yaml

@@ -16,7 +16,7 @@
   Output: "Visits to a web site tend to occur independently, one at a time, at a certain average rate. The Poisson distribution describes random processes of this type. A Poisson process is characterized by a single parameter, the expected rate of occurrence, which is usually called lambda. In our case, lambda will be expected visits per day. Of course, as the web site becomes more popular, lambda will grow. In other words, our lambda will depend on time. We will use Poisson regression to model this dependence."
 
 - Class: cmd_question
-  Output: "Somwhat remarkably, the variance of a Poisson process has the same value as its mean, lambda. You can quickly illustrate this by generating, say, n=1000 samples from a Poisson process using R's rpois(n, lambda) and calculating the sample variance. For example, type var(rpois(1000, 50)). The sample variance won't be exactly equal to the theoretical value, of course, but it will be fairly close."  
+  Output: "Somewhat remarkably, the variance of a Poisson process has the same value as its mean, lambda. You can quickly illustrate this by generating, say, n=1000 samples from a Poisson process using R's rpois(n, lambda) and calculating the sample variance. For example, type var(rpois(1000, 50)). The sample variance won't be exactly equal to the theoretical value, of course, but it will be fairly close."  
   CorrectAnswer: 'var(rpois(1000, 50))'
   AnswerTests: expr_uses_func('var');expr_uses_func('rpois')
   Hint: Try typing var(rpois(1000, 50)).

Regression_Models/Overfitting_and_Underfitting/lesson.yaml

@@ -93,7 +93,7 @@
   Hint: "Enter deviance(fit3) at the R prompt."
 
 - Class: cmd_question
-  Output: "In the next several steps, we will show how to calculate the F value, 20.968, which appears in the table printed by anova(). We'll begin with the denominator, which is fit3's residual sum of squares divided by its degrees of freedom. Fit3 has 43 residual degrees of freedom. This figure is obtained by subtracting 4, the the number of fit3's predictors (the 3 named and the intercept,) from 47, the number of samples in swiss. Store the value of deviance(fit3)/43 in a variable named d."
+  Output: "In the next several steps, we will show how to calculate the F value, 20.968, which appears in the table printed by anova(). We'll begin with the denominator, which is fit3's residual sum of squares divided by its degrees of freedom. Fit3 has 43 residual degrees of freedom. This figure is obtained by subtracting 4, the number of fit3's predictors (the 3 named and the intercept,) from 47, the number of samples in swiss. Store the value of deviance(fit3)/43 in a variable named d."
   CorrectAnswer: d <- deviance(fit3)/43
   AnswerTests: "ANY_of_exprs('d <- deviance(fit3)/43', 'd <- deviance(fit3)/df.residual(fit3)', 'd <- deviance(fit3)/fit3$df.residual')"
   Hint: "Enter d <- deviance(fit3)/43 at the R prompt."

Statistical_Inference/T_Confidence_Intervals/lesson

@@ -105,7 +105,7 @@
   Output: The quantiles are much closer together with the higher degrees of freedom. At the 97.5 percentile, though, the t quantile is still greater than the normal. Student's Rules!
 
 - Class: text
-  Output: This means the the t interval is always wider than the normal. This is because estimating the standard deviation introduces more uncertainty so a wider interval results. 
+  Output: This means the t interval is always wider than the normal. This is because estimating the standard deviation introduces more uncertainty so a wider interval results. 
 
 - Class: text
   Output: So the t-interval is defined as X' +/- t_(n-1)*s/sqrt(n) where t_(n-1) is the relevant quantile. The t interval  assumes that the data are iid normal, though it is robust to this assumption and  works well whenever the distribution of the data is roughly symmetric and mound shaped.