---
title: "Linear regression"
author: "Alizeh Azhar"
date: "9/20/2021"
output: pdf_document
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
```

## For problem 1:

(A) the graph does not form a linear pattern as it has a strong relationship it would be best suited to model it with a curve instead of a line

(B) this graph shows a strong relationship, linear model is not reasonable in this case and would be better to model it with a curve

(C) this graph depicts a slight weaker relationship and the application of a linear model is reasonable as it forms a perfect linear pattern

(D) the graph shows a weak relationship and you could fit a line thus linear model is reasonable 

(E) this graph shows a moderate relationship it is reasonable to fit a linear model 

(F) this graph shows a moderate linear relationship thus a linear model is reasonable 

## Problem 2: OLS Exercise 8.5
(a)	Exam 2 has the strongest correlation with the final exam. This is because the plot forms a better linear pattern as compared to Exam 1. Exam 1 has many outliers while majority of the points in Exam 2 linear on or closer to the fitted line as compared to exam 1.

(B)	Exam 2 is close to final exam, the student is more prepare for Exam2 than Exam 1 because it’s the predictor of final performance.


## problem 3 
3A)	There is strong linear relationship between husband and wife age. As husband’s age increases woman’s age rises.


3(B): there is a weak positive linear relationship between husband’s and wives heights and they aren’t any outliers

3(C): the plot comparing husband and wive’s ages shows a stronger correlation 

3D)	:Conversion of units for heights from centimeters to inches does not influence the correlation between husband’s and wife’s height.

## Problem 4: OLS Exercise 8.20
0.5 shows under estimation of the incidences of skin cancer. This is because the residual is positive.

## Problem 5
5(A): please show that for the equation is written like this correction should be made 
height= 106.23 + 0.61 x girth

5(B): a change in girth by 1cm increases height by 0.61cm and when shoulder girth is 0 the height is expected to be 106.23cm

5(C)Height prediction
```{r}
height= 106.23 + 0.61*100
height
```

5(D):Residual 
```{r}
Residual = 160 - 167.23
Residual
```
The residual means that the student was 7.23 shorter than predicted 

## Problem 6 (A) 
```{r}
babies <- read.csv("https://www.openintro.org/data/csv/babies.csv")
model_babies= lm(bwt~gestation, data=babies)
model_babies
```

6 (B) Write the equation of the line using mathematical notation (2 pts).

        Birth weight =-10.06418+0.4642 X Gestation