CS 145 Lecture 26 – Arrays Cont’d
Dear students,
Today we continue looking at the data that we collected last time:
- The number of children your grandparents had (i.e., the number of parents you have plus their brothers and sisters). For example, I have two parents, three uncles, and two aunts, so I’d report 7.
- The number of children your parents had, including any half- or step-siblings, and including you. For example, I have just one brother, so I’d report 2.
We collected this data in a plain text file, and we will process it to determine the following statistics:
- the average number of children in your families
- the relative frequency of each number of children in your families
- the relationship between the number of children in the previous generation and in your own
To calculate the relationship between the two numbers, we will essentially ask this question: “Is the number of children in your family a function of the number of children in your parents’ families?” We will compute a trend line—a linear regression—that gives such a function, and we will see if it’s a good fit or not.
Linear regression is computed with the following formulae:
meanXY - meanX * meanY
m = ----------------------
meanXX - meanX * meanX
b = meanY - m * meanX
y = mx + b
We’ll plot the results and see how good a model this function is.
Next we’ll examine some other data that belongs to us: our birthdays! We will do a quick check of the canonical birthday problem:
Put n people in a room. What’s the likelihood that all have different birthdays? At what n, does it flip from unlikely to likely that there’s a shared birthday?
Do we have any shared birthdays in this class? We’ll find out. Arrays will help.
Here’s your TODO list to complete before we meet again:
- Solve two problems from Array-1 and two problems from Array-2 on Coding Bat. On a quarter sheet, write down the names of the problems you solved and at least one of the solutions.
See you next class!
P.S. Here’s the code we wrote together…
Generations.java
package lecture1109; import java.io.File; import java.io.FileNotFoundException; import java.util.Arrays; import java.util.Scanner; public class Generations { public static void main(String[] args) throws FileNotFoundException { File inFile = new File("/Users/johnch/numbers.csv"); Scanner in = new Scanner(inFile); int nsamples = in.nextInt(); int[] oldChildren = new int[nsamples]; int[] youngChildren = new int[nsamples]; for (int i = 0; i < nsamples; ++i) { oldChildren[i] = in.nextInt(); youngChildren[i] = in.nextInt(); } in.close(); // for (int i = 0; i < oldChildren.length; ++i) { // System.out.println(oldChildren[i]); // } // System.out.println(Arrays.toString(oldChildren)); int sumSoFar = 0; int sumXX = 0; int sumXY = 0; int sumX = 0; int sumY = 0; for (int i = 0; i < youngChildren.length; ++i) { sumY += youngChildren[i]; sumX += oldChildren[i]; sumXX += oldChildren[i] * oldChildren[i]; sumXY += oldChildren[i] * youngChildren[i]; System.out.println(oldChildren[i] + "," + youngChildren[i]); } double meanX = sumX / (double) nsamples; double meanY = sumY / (double) nsamples; double meanXX = sumXX / (double) nsamples; double meanXY = sumXY / (double) nsamples; double m = (meanXY - meanX * meanY) / (meanXX - meanX * meanX); double b = meanY - m * meanX; System.out.printf("y = %f * x + %f%n", m, b); // double mean = sumSoFar / (double) youngChildren.length; // System.out.println(mean); } }
Birthdays.java
package lecture1109; import java.io.File; import java.io.FileNotFoundException; import java.util.Arrays; import java.util.Scanner; public class Birthdays { public static void main(String[] args) throws FileNotFoundException { Scanner in = new Scanner(new File("/Users/johnch/birthdays.csv")); int[] counts = new int[31 * 12]; while (in.hasNextInt()) { int month = in.nextInt(); int day = in.nextInt(); int daysBeforeThisMonth = (month - 1) * 31; int i = daysBeforeThisMonth + day - 1; // increment that day's counter counts[i]++; } in.close(); System.out.println(Arrays.toString(counts)); for (int i = 0; i < counts.length; ++i) { if (counts[i] > 1) { int month = i / 31 + 1; int day = i % 31 + 1; System.out.println(month + " " + day); } } } }