A study took a random sample often married couples, and asked the husband's and wife's age. The scatterplot shows the associatio
n between the ages of the husbands and wives. Not surprisingly, older husbands tend to have older wives, so the data has a positive linear association. A researcher finds that the least squares regression equation for this relationship is ŷ= 0.89 x + 2.62.
Suppose you interview a married man who has lived to the ripe old age of 100, and still married to his wife. using the least squares regression equation, predict his wife's age.
A. 100
B. 89
C. 91.62
D. 86.38
—my answer is option (c.) 91.62
Any reviews would be much appreciated...
Suppose you interview a married man who has lived to the ripe old age of 100, and still married to his wife. using the least squares regression equation, predict his wife's age.
A. 100
B. 89
C. 91.62
D. 86.38
—my answer is option (c.) 91.62
Any reviews would be much appreciated...
2 answers:
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Answer:
See Explanation.
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
- Left to Right
Equality Properties
- Multiplication Property of Equality
- Division Property of Equality
- Addition Property of Equality
- Subtract Property of Equality
<u>Algebra I</u>
Slope Formula:
Slope-Intercept Form: y = mx + b
- m - slope
- b - y-intercept
Linear Regression
Step-by-step explanation:
We can draw any best line of fit, as long as it is <em>reasonable</em> around the points that are given.
We can just take 2 points and use slope formula and Slope-Intercept Form to find the equation for the best line of fit.
Using Linear Regression, we can determine the <em>true</em> best line of fit using graphing utilities.
<u>Finding the best line of fit</u>
<em>Define 2 points</em>
Point (21600, 205)
Point (27000, 290)
<em>Find slope m</em>
- Substitute in point [SF]:
- [Fraction] Subtract:
- [Fraction] Simplify:
<em>Find equation</em>
- Define equation [SIF]:
- Substitute in point:
- Multiply:
- Isolate y-intercept <em>b</em>:
- Rewrite:
- Redefine equation:
Slope-Intercept Form tells us that our slope <em>m</em> = and our y-intercept
.
Setting this as function f(x), we can see from the graph that it is extremely accurate (Blue line).
<u>Using Linear Regression</u>
Depending on the graphing calc you have, the steps may be different.
Using a graphing calc, we can use statistics and determine the <em>best</em> best line of fit.
When we determine the values, we should see that our equation would be g(x) (Green Line).
<em>Credit to Lauren for collabing w/ me in graphing.</em>
