1 2 3 4 5 6 7 8 80 95 75 82 95 95 90 88 86 97 85 91 100 90 94 93 Student Quiz Grades Test Grades 1. Describe the association between Quiz Grades and Test Grades. 2. Write the equation of the line of regression. 3. Use this model to predict a test grade based on a quiz grade of 82. 4. What is the Residual for the quiz grade of 82? 5. Is this a good model? Quiz Grade Test Grade Quiz Grade Residuals Test Grade = 44.691 + 0.541(Quiz Grade) Test Grade = 44.691 + 0.541(Quiz Grade) = 44.691 + 0.541(82) = 44.691 + 0.541(82) 89.026 89.026 WARM – UP r = 0.815 r = 0.815 Resid=y – y Resid=y – y Resid=91-89.026 Resid=91-89.026 Resid=1.974 Resid=1.974
Transcript
1 2 3 4 5 6 7 8
80 95 75 82 95 95 90 88
86 97 85 91 100 90 94 93
Student
Quiz Grades
Test Grades
1. Describe the association between Quiz Grades and Test Grades.2. Write the equation of the line of regression.3. Use this model to predict a test grade based on a quiz grade of 82.4. What is the Residual for the quiz grade of 82?5. Is this a good model?
WARM – UPThe Statistics had an average of 81.2 with a standard deviation of 4.5. a.) What score represents the 90th percentiles?
b.) What is the probability that at least 3 out of 8 randomly selected students scored in the top 10%.
c.) Assuming a Normal Distribution, what is the probability that a random sample of 3 students will have a mean score of at least 85?
z = InvNorm(0.90) = zx 1.282
81.21.282
4.5x x = 86.969
( 3)P x 1 ( 2)P x 1 (8, , 2)Binomialcdf 0.10 = 0.0381
( 85)P x 85 81.2
( )4.5 / 3
P z
n
zx
( 1.463)P z
Prob. = Normalcdf(1.463,∞) = 0.0718
WARM – UP
Many Economist believe that the down turn of the US Economy is due to developments in the Housing Market. The table below indicates random Medium home prices and the Unemployment Rate at that time.
3/07 6/07 10/07 12/07 5/08 7/08 11/08 1/09
263 236 234 228 229 221 225 201
4.40 4.50 4.70 5.00 5.50 5.70 6.70 7.60
DATE
Housing $100K
Unemployment Rate
1. Describe the association between Housing values and Unemployment.
2. Write the equation of the line of regression.3. Use this model to predict unemployment if housing
reaches $180,000.4. Is this a good model?
3/07 6/07 10/07 12/07 5/08 7/08 11/08 1/09
263 236 234 228 229 221 225 201
4.40 4.50 4.70 5.00 5.50 5.70 6.70 7.60
DATE
Housing $100K
Unemployment Rate
1. Describe the association between Housing values and Unemployment.2. Write the equation of the line of regression.3. Use this model to predict unemployment if housing reaches $180,000.4. Is this a good model?
Does a significant relationship exist between number of hours studying and test grades? 63.663 11.371( )Grade hours
1 1.6803SE b 11.371 0
1.6803t
2 ( 6.767 , 99, 4)P Value tcdf E 0.0025
H0: β1 = 0
Ha: β1 ≠ 0
Chapter 27 – INFERENCE FOR REGRESSION
– Spread around the line = sSpread around the line = see:
• The spread around the line is measured with the standard deviation of the residuals ssee.
Chapter 27 – INFERENCE FOR REGRESSION
– Spread of the x values = sSpread of the x values = sxx:
• A large standard deviation of x provides a more stable regression.
– Spread around the line = sSpread around the line = see
– Sample Size = nSample Size = n
– Spread of the x values = sSpread of the x values = sxx
11e
x
sSE b
n s
SE(b1) is the Standard Error about the slope.
β = 0 A Linear Relationship
does NOT exist
β ≠ 0 A Linear Relationship
does exist
1
1
0btSE b
LINEAR REGRESSION t – TESTUsed to determine whether a significant relationship exists between two quantitative variables.
/
xt
s n
WARM – UPMany Economist believe that the current situation of the US Economy is due to developments in the Housing Market. The table below indicates random Medium home prices and the Unemployment Rate at that time.
