TASK $1$: Linear Regression $(15\%-100$ marks$)$

This task will test your knowledge of file input and mathematical formulas. Basic linear regression

$($LR$)$ is used to find a relationship between two types of data. For example, you could use LR to find

the relationship between glucose intake and heart rate. These initially would be plotted on a graph

where the $x$ axis represents glucose and the $y$ axis represents heart rate. Using the LR formula, you

can find $y=bx+a($equation of a straight line $($more commonly known as $y=mx+c)$ between $"n"$

number of points on a graph. Below are the formulas to find $"$a$"$ and $"$b$."$

$A=\frac{(y)(x^2)-(x)(xy)}{n(x^2)-(x{)}^2}$

$B=\frac{n(xy)-(x)(y)}{n(x^2)-(x{)}^2}$

You will be given multiple text files containing $"n"$ number of coordinates. Your program will read in

the coordinates $(x,y)$ and use the LR formula to produce the gradient $($a$)$ and the constant $($b$),$ and

being able to print out $y=bx+a.$ For example, if $a=0\mathrm{.}5$ and $b=-2,$ your program will print out

$y=-2x+0\mathrm{.}5.$ This equation now represents the trend in the data you will be given. Finally, your

program will ask the user to type in a value of $x$ which will then calculate $y.$

Read data from file appropriately $(30$ marks$)$

Use LR formula to process the data and print out the correct equation of a straight line $(50$

marks$)$ Find new value of $"y"$ using user input $(20$ marks$)$