6.09 Fit a Line to Data

Fit a Line to Data

6.09

Dropdown

Marie joined the track team and began training for the 200 m sprint. The graph shows her lowest time each week since she began training. The line models the relationship between the number of weeks Marie spent training and her lowest recorded time running the 200 m sprint. The equation of the line is y=−0.4x+29.8. The slope and association of this line

Select answer

. This means that as Marie trains, her time​

Select answer

.

In some paired data sets, one variable depends on, or can be explained by, the other. The explanatory variable, or input variable, is the independent variable, x. The response variable or output variable, is the dependent variable, y. 

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Key Concept

Multiple Select

What is another name for the Explanatory Variable ? Select all that apply

• Input variable

• Output variable

• x

• y

Multiple Select

What is another name for Response Variable? Select all that apply

• Dependent variable

• Output variable

• x

• y

Match

Determine whether the variable is explanatory, response, or neither.

cost of a car collision repair and the speed of the car before the collision

• cost of car collision repair

• speed of the car before collision

• color of car

response

explanatory

neither

• response

• explanatory

• neither

Match

Determine whether the variable is explanatory, response, or neither.

the number of vacation days an employee has and the number of years the employee has worked for that employer

• number of vacation days

• number of years employed for that employer

• floor employee works on

response

explanatory

neither

• response

• explanatory

• neither

It is useful to determine the equation of a regression line because you can use it to draw conclusions and make predictions. You can determine the equation by using two points on, or near, the line and the point-slope form (of a linear equation).

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Key Concept

The equation yˆ=125x−900 describes the trend of the data in the scatter plot. The slope gives the amount of change in the response variable for one unit of change in the explanatory variable. So the slope of 125 means that a person can expect to earn an additional $125/wk for each additional year of education achieved.

Fill in the Blanks

Use substitution in the regression line
yˆ=125x−900

to predict how much someone with 17 years of schooling would make per week

Multiple Choice

Using point-slope form for point (22, 23) and slope -1, which equation is accurate?

• y - 23 = -1(x - 22)
• y - 23 = 1(x - 22)
• y + 23 = -1(x + 22)
• y - 23 = -2(x - 22)

Fill in the Blanks

Now that you've found the regression line in point slope form, convert y - 23 = -1(x - 22) to slope-intercept form:

do not use spaces in your answer

Poll

Much of what we covered today is a review of a lot of things we've already seen this year. That being said, what's your next step?

• If there was a quiz, I'd be ready for it.

• I think I have it, but will need to review the practice section of 6.09

• I'm feeling a little lost. I'll be reading the entire 6.09 lesson.

• I've already read the lesson and I'm still completely lost. I will book a 1:1 with you.