Question

1. In the R programming language, we would like to use the data set called iris to build a simple linear regression model to predict

Sepal.Length based on Petal.Length.

1. Calculate the least squares regression line to predict Sepal.Length based on Petal.Length. Interpret the slope of the line in the context of the problem. Remember that both variables are measured in centimeters.
2. Plot the regression line in a scatterplot of Sepal.Length vs. Petal.Length.
3. Test H1: ??₁ ≠ 0 at ?? = 0.05 using both a ??-test and an ??-test. Report the test statistics and interpret the results.
4. Visually check the normality assumption. Does it seem reasonable here?
5. Visually check the constant variance assumption. Does it seem reasonable here?
6. Interpret this regression model’s ??².
7. Using the regression line, what would you predict as the Sepal.Length for an iris with a Petal.Length of 3.4 cm?
8. We would expect approximately 95% of the irises to have a Sepal.Length within ± (fill in the blank)  cm of their predicted values from the regression line.

Answers should be in the form of R code on how to accomplish each part and include the correct statistical explanation for those that require it in the question. Please be as thorough as possible. Thank you so much!!!

Answer 1

a)

The linear regression equation is

Y=4.3066+0.40892X      where Y= Sapel length and X= Petal length

Slope of the line is 0.40892

i.e for every 1 cm increase in petal length there is 0.40892cm lenth in Sapel length.

b)

c) H0:

    H1:

t -value = 21.65    (refer R code)

Since p-value<0.05 we reject H0 and conclude that there is significant releation between Petal length anf Sapel length

F-value=468.6

p-value <0.05 hence reject Ho that there is no relationship between petal length and Sapel length.

g) the Sapel length when the petal length is 3.4 cm is

d and e)

In Q-Q plot we have diogonal line, hence the data is normally distributed.

In the scale location graph the points are equally spread below and above the red line. Hence we can assume constant variance.

f) the adjusted R-square is 0.758 . That means 75.8% of changes in sapel length is dependend on petal length.

h)