Math Problem Statement
What is the least-squares regression line with the point left parenthesis 9 comma 13 right parenthesis included in the data set?
Data Set
x
y
3
6
4
5
5
7
6
4
7
6
8
9
8
8
10
8
11
9
11
7
12
10
13
12
13
10
14
11
(This is a reading assessment question. Be certain of your answer because you only get one attempt on this question.)
.
.
.
Question content area right
Part 1
ModifyingAbove y with caretequals
enter your response herexplus
enter your response here
(Type integers or decimals rounded to four decimal places as needed.)
Solution
To find the least-squares regression line, we first need to calculate the slope and the y-intercept of the line . The formulas for the slope and intercept are:
where:
- is the number of data points
- is the sum of all -values
- is the sum of all -values
- is the sum of the product of each and
- is the sum of the squares of each
Step 1: Calculate the necessary sums.
Given the data set (including the point ):
- Calculate , , , , and :
Step 2: Calculate the slope and intercept .
Using the formulas:
Step 3: Write the equation of the least-squares regression line.
The equation is:
Rounding the slope and intercept to four decimal places, the least-squares regression line is approximately:
Would you like further details or have any questions about this calculation?
Related Questions:
- How does including an outlier affect the least-squares regression line?
- What is the meaning of the slope in a least-squares regression line?
- How can you determine if a least-squares regression line is a good fit for the data?
- What is the interpretation of the y-intercept in a regression line?
- How do you calculate the coefficient of determination, , for this data set?
Tip:
When rounding intermediate calculations, keep more decimal places than the final answer to avoid rounding errors in the final result.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Statistics
Linear Regression
Algebra
Formulas
Slope formula: m = [n(∑xy) - (∑x)(∑y)] / [n(∑x^2) - (∑x)^2]
Y-intercept formula: b = [∑y - m(∑x)] / n
Least-squares regression line formula: ŷ = mx + b
Theorems
Least-Squares Regression Theorem
Suitable Grade Level
Grades 10-12
Related Recommendation
Linear Regression Line Calculation for Points (5, 5), (7, 7), (9, 10)
Linear Regression Line for Points (3, 4), (6, 6), (9, 9)
Least-Squares Regression Equation for Given Dataset
Find the Line of Best Fit and Intercept Using Least Squares Regression
Linear Regression for Data Points (Calculate Slope and Intercept)