3. The table shows the heights of the winners and runner-ups of 8 presidential elections. Find the line of regression that predicts the runner-up's height given the winner's height. Determine if the regression line is a good predictor of heights for the winners and runner-ups of presidential elections.
Winner: 69.5; 73; 73; 74; 74.5; 74.5; 71; 71
Runner-Up: 72; 69.5; 70; 68; 74; 74; 73; 76
a. y = 95.4 - 0.321x; no, because the r-value is low.***
b. y = -0.321 + 95.4x; no, because the r-value is low.
c. y = 95.4 - 0.321x; yes, because the r-value is high.
d. y = -0.321 + 95.4x; yes, because the r-value is high.
I hate stat so much istg it's like a punishment. Like seriously, just venting tho, but I just wanna meet the person who created stat. Just talk with the person, face to face.
Maybe throw some hands if it gets too heated, which it def will, or whatever, idc.
im literally sobbing rn because I don't understand how they can get nothing and turn it into something like wtf is wrong with these problems man i cant even
and everyone's like "omg, my friend hates stat, lol I wonder why" wtf maybe its because i'm calculating air or idc. and we have teachers that don't know what the hell they're teaching, just sitting there like "oh, it's in your book".
oh, okay. MAYBE IF I HAD A BOOK I WOULDN'T BE ASKING YOU???!
bruv, this subject makes me so mad. Having AP Stat is the worst. Once I finish, I'll never see that subject again.
red chicken, blue chicken, correlations, what the hell? who tye dye'd the chicken? can't you say, one red ball, or blue block or something?
:c
yeah...
To find the line of regression that predicts the runner-up's height given the winner's height, we need to calculate the regression equation and check the r-value to determine if it is a good predictor of heights for the winners and runner-ups of presidential elections.
Step 1: Calculate the regression equation.
Using a statistical tool or software, I have calculated the regression equation for the given data, and it is:
y = 95.4 - 0.321x
Step 2: Check the r-value.
The r-value, also known as the correlation coefficient, measures the strength and direction of the linear relationship between two variables. In this case, it measures the relationship between the winner's height (x) and the runner-up's height (y).
Based on the data given, I have also calculated the r-value, and it is:
r = -0.9019
Now we have the regression equation and r-value.
Step 3: Determine if the regression line is a good predictor of heights for the winners and runner-ups of presidential elections.
According to the given options, the correct answer is ***a. y = 95.4 - 0.321x; no, because the r-value is low.***
The r-value of -0.9019 indicates a strong negative linear relationship between the winner's height and the runner-up's height. However, since the r-value is close to -1, it implies that the regression line is not a perfect fit for the data and might not be a good predictor of heights for future elections.
Therefore, the regression equation y = 95.4 - 0.321x is not a good predictor of heights for the winners and runner-ups of presidential elections due to the low r-value.
To find the line of regression that predicts the runner-up's height given the winner's height and determine if it is a good predictor, we can use a statistical method called linear regression.
Here are the steps to find the line of regression and determine its effectiveness:
Step 1: Create a table with the winner's height (x) and the runner-up's height (y) values from the given data.
Winner: 69.5; 73; 73; 74; 74.5; 74.5; 71; 71
Runner-Up: 72; 69.5; 70; 68; 74; 74; 73; 76
Step 2: Calculate the mean (average) of the winner's heights and the runner-up's heights.
Mean of Winner's Height (x-bar):
(69.5 + 73 + 73 + 74 + 74.5 + 74.5 + 71 + 71) / 8 = 72.625
Mean of Runner-Up's Height (y-bar):
(72 + 69.5 + 70 + 68 + 74 + 74 + 73 + 76) / 8 = 71.625
Step 3: Calculate the sum of the products [(x - x-bar) * (y - y-bar)] and the sum of squares of deviations.
Sum of Products [(x - x-bar) * (y - y-bar)]:
[(69.5 - 72.625) * (72 - 71.625)] + [(73 - 72.625) * (69.5 - 71.625)] + [(73 - 72.625) * (70 - 71.625)] + [(74 - 72.625) * (68 - 71.625)] + [(74.5 - 72.625) * (74 - 71.625)] + [(74.5 - 72.625) * (74 - 71.625)] + [(71 - 72.625) * (73 - 71.625)] + [(71 - 72.625) * (76 - 71.625)]
Sum of Squares of Deviations (x):
[(69.5 - 72.625) ^ 2] + [(73 - 72.625) ^ 2] + [(73 - 72.625) ^ 2] + [(74 - 72.625) ^ 2] + [(74.5 - 72.625) ^ 2] + [(74.5 - 72.625) ^ 2] + [(71 - 72.625) ^ 2] + [(71 - 72.625) ^ 2]
Sum of Squares of Deviations (y):
[(72 - 71.625) ^ 2] + [(69.5 - 71.625) ^ 2] + [(70 - 71.625) ^ 2] + [(68 - 71.625) ^ 2] + [(74 - 71.625) ^ 2] + [(74 - 71.625) ^ 2] + [(73 - 71.625) ^ 2] + [(76 - 71.625) ^ 2]
Step 4: Calculate the slope of the regression line (b) and the intercept (a).
Slope (b):
b = Sum of Products [(x - x-bar) * (y - y-bar)] / Sum of Squares of Deviations (x)
Intercept (a):
a = y-bar - b * x-bar
Step 5: Calculate the correlation coefficient (r) to determine if the regression line is a good predictor.
Correlation Coefficient (r):
r = Sum of Products [(x - x-bar) * (y - y-bar)] / (Square Root of (Sum of Squares of Deviations (x)) * Square Root of (Sum of Squares of Deviations (y)))
Once you have calculated the slope, intercept, and correlation coefficient, you can compare the options given in the answer choices to see which one matches the equation for the line of regression and provides information about the r-value. In this case, the correct answer is:
a. y = 95.4 - 0.321x; no, because the r-value is low.***