Question

In: Statistics and Probability

7. In full sentences, what is a simple linear regression? 8. In full sentences, what is...

7. In full sentences, what is a simple linear regression?
8. In full sentences, what is the “Line of Best Fit or Least-Squares Line”?
9. The table below show the average heights for American girls as of 2018.
Age (years) Height (cm)
birth 49.2
2 85.5
5 107.9
10 138.4
15 159.7
18 163
20 163.3
https://www.disabled-world.com/calculators-charts/height-weight-teens.php
a. Decide which variable should be the independent variable and which should be the dependent variable.
b. Draw a scatter plot of the data.
c.  Does it appear from inspection that there is a relationship between the variables? Why or why not?
d. Calculate the least-squares line. Put the equation in the form of: ? = a + bx
e. Find the correlation coefficient. Is it significant?
f. Find the estimated average height for a one-year-old. Find the estimated average height for a 21-year-old.
g. Does it appear that a line is the best way to fit the data? Why or why not?
h. Are there any outliers in the data?
i. Use the least squares line to estimate the average height for a fifty-year-old woman. Do you think that your answer is reasonable? Why or why not?
(Hint: how tall was the tallest woman ever recorded?)
j. What is the slope of the least-squares (best-fit) line? Interpret the slope.

Solutions

Expert Solution

Solution7:

In simple regression a single variable X is used to define/predict Y.

Y is called dependent variable

X is called independent variable.

simple regression is

y=b0+b1x

bo is called y intercept

b1 is slope of regression line

Solution8:

it is the process of trying to fit the best staright line to a set of data.

the usual method is based on minimising the squares of the errors between the data and the predicted line.

the method of estimating the parameters slope and y intercept is the least squares method i.t the line of best fit.

minimising the sum of the vertical distances of each value from the staright line drawn.

Minimising the sum of the squared errors.

orchestra answered 1 year ago
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