Introduction to Regression

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Show your work for each problem.

1.
What does the represent in the equation ?
1. a)The x-value
2. b)The slope (rate of change)
3. c)The y-intercept
4. d)The prediction
2.
What is the purpose of linear regression?
1. a)To calculate the average of numbers
2. b)To find the best-fitting line through data points
3. c)To count how many data points exist
4. d)To find the largest value in a dataset
3.
For the equation , what is the slope?
4.
For the equation , what is the y-intercept?
5.
Using the equation , find when .
6.
Calculate the slope between points and .
1. a)8
2. b)4
3. c)2
4. d)0.5
7.
Calculate the slope between points and .
8.
Find the equation of the line through points and .
9.
A regression model shows that test scores increase by 8 points for each hour of studying. A student who studies 0 hours scores 40 points. Write the equation and predict the score for 5 hours of studying.
10.
A regression line has a negative slope. What does this mean?
1. a)As x increases, y decreases
2. b)The line passes through the origin
3. c)As x increases, y increases
4. d)The data has no relationship
11.
Find the equation of the line through points and .
12.
A car's fuel efficiency is modeled by , where is the car's weight in kg and is km/L. What is the predicted fuel efficiency for a car weighing 1000 kg?
13.
Find the equation of the line through points and .
14.
Why is it problematic to use a regression equation to predict values far outside the original data range?
1. a)The slope changes automatically
2. b)The equation becomes mathematically invalid
3. c)The y-intercept shifts
4. d)The relationship may not continue linearly beyond the data
15.
A house pricing model shows , where is square meters and is price in euros. Find the predicted price for a 120 m² house, and interpret what the slope means.
16.
Two students measured height and shoe size. Student A found a slope of 0.5, and Student B found a slope of 2.0. Both measured the same people. What could explain this difference?
1. a)The data changed between measurements
2. b)They measured at different times
3. c)One made calculation errors
4. d)They used different units for measurement