Hodge Podge
Regression from Outputs
Residuals
Scatterplots
Hypothesis Tests/ Confidence Intervals
100
The average softball pitcher throws at 55mph with a standard deviation of 4mph. The average speed a ball comes off a softball bat is 70mph with a standard deviation of 5mph. The correlation between speed off a bat and speed thrown is 0.82. Find the slope of the line that would predict the speed a ball comes off the bat from the speed the ball is thrown.
b = 0.82(5/4) = 1.025
100
Find the line of best fit for newborn heartrate based on amount of sodium
y-hat = 147.1427 + 0.2457x
y-hat - predicted heart rate
x - amount of sodium
100
What three things do we use to describe residuals?
Small, Random and Balanced.
100
Esimate the R -value
.5 - .7
100
What is the formula for degrees of freedom for a linear regression t-test or confidence interval?
df = n-2
200
You are given 3 graphs with the following r-values, which is the strongest linear relationship?
A -0.85
B 0.72
C 0.25
A (absolute value closest to 1)
200
Interpret the y- intercept for newborn heartrate based on amount of sodium
If a newborn has no sodium, there heartrate is 147.1427
200
If you have a negative residual, did you over or under estimate the orgiinal value?
(Actual - predicted) Over estimated
200
Estimate the r-value
0
200
Create the 95% confidence interval for slope for the following with an n = 15
1.6370+-(2.160)(0.5453) = (0.459, 2.815)
300
The coefficient of variation must be between what two numbers?
0<=r^2<=1
300
Interpret the slope
For each calorie increase in the sandwich, the protein will increase by about 0.06515 grams.
300
Your line of best fit is given by y-hat = 13+3.2x. The actual point on the line is (10, 42). Find the residual for this point.
-3
13+3.2(10) = 45
42-45 = -3
300
What is the name of point A?
Outlier
300
An organization is interested to see the more beers consumed will increase a person's blood alchol content (BAC). 16 volunteers were randomly given a number of beers to drink and 30 minutes later a police officer tested their BAC. Write the null and alternative hypothesis for the situation.
H_0:B = 0 H_A: B>0
400
The equation to predict final exam scores from the first test score is y-hat = 10+0.9x. If a student scored a 95 on the first test, what is the predicted final exam score?
95.5
400
What is the coefficient of determination?
0.399
400
What does this residual plot tell you about the linear model?
A linear model is not appropirate for this data set since the data is not random (there is a curved pattern).
400
Describe the association in context
As hours spent studying increase, percentage on math test appears to increase.
400
What is the t-value for the hypothesis test from the computer output below.
t = 3.68 (2.4599/0.6669)
500
Find the line to predict repair cost from number of car washes
y-hat = 1344.16 - 60.76 x
x = number of car washes
y-hat =predicted repair cost
500
What is the correlation coefficient?
-0.815
500
What is required of residuals in order to run a hypothesis test for slope?
Nearly normal shape AND equal variance
500
What is the name of the red point and what effect does it have on the r-value?
Influential point. Here is raises the r-value (closer to 1)
500
What are the 5 conditions for inference for linear regression?
1. Linear
2. Independent
3. Nearly normal residuals
4. Random
5. Equal variance (no fanning)