Statistics help - Scatter plot, regression

AI Thread Summary
The discussion focuses on analyzing a dataset of first-grade students' spelling test performance based on the time spent studying. A strong positive correlation is observed, with a correlation coefficient of approximately -0.7698, indicating a significant relationship between study time and errors made. The regression line is defined by the equation y = -0.4096x + 19.1903, allowing predictions of errors based on study time. For a student studying for 32 minutes, the predicted number of errors is approximately 6.08, with a residual of about 1.92 when the actual number of errors is 8. The conversation highlights the importance of understanding regression analysis and its application in predicting outcomes.
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Statistics help -- Scatter plot, regression

Homework Statement



Consider the following data set for ten first grade students; the variables are the number of minutes spent learning a list of spelling words and the number wrong on the spelling test. [15 points total]

(supposed to be a chart)
STUDENT A B C D E F G H I J
MINUTES 25 28 30 31 31 35 36 38 40 50
WRONG 12 10 8 1 6 4 4 3 2 1


a. Describe the scatter plot: form, direction, and strength. [3 points]
b. Determine the value of the correlation coefficient.
c. Determine the value of the coefficient of determination (state as a percent).
d. Find the slope of the best fitting regression line for predicting number wrong.
e. Find the intercept of this regression line.
f. Present the equation of this best fitting regression line.
g. If another student now studies the list for 32 minutes, use the equation to predict his number wrong.
h. If that student’s actual number wrong is 8, determine the residual associated with this prediction.
i. Plot the regression line on your scatterplot. (submit this plot)
j. Are there any outliers? If so, give the coordinates.
k. Are there any influential points? If so, give the coordinates.
l. Suppose another student studies the list for 60 minutes. Predict his number wrong.
m. Comment on this prediction.


Homework Equations


y = mx+b
y-b=mx
??

The Attempt at a Solution



a.strong; positive
b. 4.65
c. 68%
d. ?
e. 30
f. 28
g. ?
h. ?
I don't understand how to do this, please help:(
 
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Calculator14 said:

Homework Statement



Consider the following data set for ten first grade students; the variables are the number of minutes spent learning a list of spelling words and the number wrong on the spelling test. [15 points total]

(supposed to be a chart)
STUDENT A B C D E F G H I J
MINUTES 25 28 30 31 31 35 36 38 40 50
WRONG 12 10 8 1 6 4 4 3 2 1


a. Describe the scatter plot: form, direction, and strength. [3 points]
b. Determine the value of the correlation coefficient.
c. Determine the value of the coefficient of determination (state as a percent).
d. Find the slope of the best fitting regression line for predicting number wrong.
e. Find the intercept of this regression line.
f. Present the equation of this best fitting regression line.
g. If another student now studies the list for 32 minutes, use the equation to predict his number wrong.
h. If that student’s actual number wrong is 8, determine the residual associated with this prediction.
i. Plot the regression line on your scatterplot. (submit this plot)
j. Are there any outliers? If so, give the coordinates.
k. Are there any influential points? If so, give the coordinates.
l. Suppose another student studies the list for 60 minutes. Predict his number wrong.
m. Comment on this prediction.


Homework Equations


y = mx+b
y-b=mx
??

The Attempt at a Solution



a.strong; positive
b. 4.65
c. 68%
d. ?
e. 30
f. 28
g. ?
h. ?
I don't understand how to do this, please help:(

Welcome to the PF.

Can you please show us your work on the answers that you were able to calculate? That will help us a lot. Thanks.
 


my work for this problem is..

b) -.4096 = (3.8137/7.1678) r
r = -.7698

c) (-.7698)^2

d) y= -.4096x +19.1903

e) m=-.4096

f) y = -.4096x = 19.1903

g) y = -.4096 (32) + 19.1903
y=6.0831

h) 8 - 6.0831 = 1.9169

i) ?

j) (31,1)

k) graphed

l) y= -.4096(60) + 19.1903 = -5.3857

m)?
 
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