Here is some fictional data for a set of BMX bikes showing their weight and maximum number of inches a rider was able to get them in the air for a trick.
Enter the data into L1 and L2.
Create a scatter plot. Observe the relationship between weight of the BMX bike and the height of the jump.
What did you use as your explanatory variable? Why?
Question 1
1.
Question 2
2.
Question 3
3.
Question 4
4.
Question 5
5.
Check the model you have chosen by doing the regression.
Be sure to store your regression equation and record the a & b values.
a =
Round to three places past the decimal.
Question 6
6.
b =
Round to three places past the decimal.
Question 7
7.
Check the residual plot, draw it in the 'show your work' area using the line tool.
Question 8
8.
Based on the residuals, is the linear model is appropriate?
(the residuals should look fairly random)
Question 9
9.
Write the linear regression model below, be sure to use correct notation and meaningful words.
No spaces, round a and b to three places past the decimal.
Use 'height' and 'weight' for the variable names.
Question 10
10.
Use your model to predict the height that a 25 pound bike can jump.
Round to two places past the decimal.
Question 11
11.
Question 12
12.
Use your model to predict the height that a 20.5 bike can jump.
Round to two places past the decimal.
Question 13
13.
Foot lenght(in cm) was used to predict the height(in cm) of students, data was entered and a regression was calculated using the computer output information below.
Question 14
14.
What is the explanatory variable?
Question 15
15.
What is the response variable?
Question 16
16.
Create a Linear Regression equation for the Line of Best Fit for the relationship between foot length(cm) and height(cm).
Round decimals to two places past the decimal point.
Use 'height' and 'length' for the variable names.
Be sure to indicate which variable is being predicted.
No spaces.
Question 17
17.
Question 18
18.
Question 19
19.
Predict the height of someone with a 29.5 cm foot:
Question 20
20.
Question 21
21.
Use the computer output to determine the correlation coefficient:
Round to three places past the decimal.
Bacteria have the ability to multiply at an alarming rate, where each bacteria splits into two new cells, doubling the number of bacteria present.
NOTE:
for x=4, y should equal 1200 (NOT 12000) that is MY mistake. Sorry about that!
Question 22
22.
Question 23
23.
Question 24
24.
Question 25
25.
Write the regression equation below.
Use 'hours' and 'bacteria' for the variable names.
No spaces.
Round decimals to two places.
Question 26
26.
Question 27
27.
Use your regression equation to predict the number of bacteria that will be present after 3.5 hours:
Round the decimal to two places.
Question 28
28.
Predict the number of bacteria that will be present after 24 hours:
Round to two places past the decimal.
Question 29
29.
Use the following data table, enter the values into L1 and L2.
Question 30
30.
Create a scatter plot of the data.
Do a linear regression, stat calc #8
Enter the R-squared value:
Round to four places past the decimal
Question 31
31.
Do an exponential regression, stat calc #0
Enter the R-squared value:
Round to four places past the decimal
Question 32
32.
Do a power regression, stat, calc, alpha, math
Enter the R-squared value:
Round to four places past the decimal
Question 33
33.
Question 34
34.
Question 35
35.
Question 36
36.
Question 37
37.
What did you use as your explanatory variable? Why?
Height of the jump
Weight of the bike affects the height of the jump.
Weight of the BMX bike
Height of the bike affects the weight of the bike.
Describe the relationship you see between weight and height in the scatter plot (Form, Direction & Strength).
Strong Curve
Nearly Linear
Scatter, no association
Strong
Moderate
Weak
Negative
Positive
No Direction
Give the verbal description of the relationship in this context between the weight of a bike and the height of the jump it is able to reach.
As the weight of the bike increases the height of the jump increases.
As the weight of the bike increases the height of the jump decreases.
As the weight of the bike increases the height of the jump is not affected.
Based on the scatterplot, which model seems to be more appropriate? Why?
The form is strongly curved
Power
The form is random scatter.
Exponential
Linear
The form is Nearly Linear
Do you have confidence in this prediction?
Why or why not?
What is this called?
Not a lot
Yes
I'm not sure
We are predicting beyond the range of the x values for our data.
We are predicting beyond the range of the y values for our data.
We are predicting within the range fo the x values for our data.
Extrapolation
Interpolation
Calculate the residuals for the 20.5 bike using information from the table.
What does this tell us about the model?
0.04
-0.04
The model over predicted the height of the jump.
The model under predicted the height of the jump.
Interpret the meaning of the slope in this context:
Use numbers!
For every 1 cm. increase in height the foot length increases by 2.75 cm.
For every 1 cm increase in foot length the height increases by 2.75 cm.
As the length increases the height increases.
As the height increases the length increases.
Interpret the meaning of the y-intercept if it has one:
The y-intercept has no meaning in this situation, someone can't have a foot that is 0 cm long.
Someone with a foot that is 0 cm long will be 103.41 cm tall.
Someone with a foot that is 0 cm long will be 2.75 cm tall.
If the person from g was actually 180.3 cm, what is the residual? What does this tell us about the model?
-4.235
4.235
The model over predicted the height.
The model under predicted the height.
Enter the data into L1 and L2 on your calculator, create a scatterplot.
Describe the relationship. Which model will you use?
Nearly Linear
Curved
Random Scatter
Strong
Moderate
Weak
Negative direction
Positive direction
No direction
Which model will you use?
Why?
The scatterplot looks nearly linear.
Exponential
The scatterplot looks curved.
Linear
Do a regression for your model,
store the regression equation and observe the residual plot.
What do you see and what does this mean?
The exponential regression may not be appropriate in this situation.
A curved pattern in the residuals
Random scatter
The exponential regression is appropriate in this situation.
Describe the rate in the context of the bacteria growth:
The bacteria population grows by 1.19% for each hour that passes.
The bacteria population grows by 19% for each hour that passes.
The bacteria populatin shrinks by 1.19% for each hour that passes.
The bacteria population shrinks by 19% for each hour that passes.
For which prediction do you have the least confidence?
Why?
What is a prediction outside the range of our data values called?
Interpolation
Extrapolation
3.5 hours
24 hours
The further our explanatory value is from the data values the weaker the prediction.
If our explanatory value within our explanatory data range we don't have confidence in the prediction.
Based on the coefficient of determination (R-squared), which regression model is the most appropriate for the data set?
Why?
Linear
Exponential
Power
The R-squared is the closest to 1.00
The R-squared is the closest to 0.00
A residuals plot is useful because
I. it will help us to see whether our model is appropriate for making predictions.
II. it might show a pattern in the data that was hard to see in the original scatterplot.
III. It shows the residual for each data point.
I
II
III
None are true
Although there are annual ups and downs, over the long run, growth in the stock market averages about 9% per year.
A model that best describes the value of a stock portfolio is probably:
Linear
Exponential
Power
Can't be determined
A business owner notes that for every extra hour his store is open, his total sales increase by a fixed amount. His most useful predictive model is probably…
Linear
Exponential
Power
Cant be determined
What are some of the effects of outliers in a scatterplot:
Outliers strengthen the relationship, making the correlation coefficient closer to +1 or -1
Outliers weaken the relationship, making the correlation coefficient closer to 0