Problem 1
Problem 1
Compute sample co
elation coeeficient and the coefficients for the least-squares regression line
Given the following data We want to predict the selling price of a house in Newburg Park FL
based on the distance the house lies from the beach.
Distance from the beach, x (in miles) Selling price, y (in thousands of dollars)
6.2 302.7
18.5 216.3
8.5 250
8.3 292.3
4.1 308.5
4.9 264.8
11.6 227
13.8 265.5
13.5 196.6
13.2 188
10 274.4
7.4 234.3
6.2 270.8
5.7 216.4
10.9 197.3
9.2 290.2
What is the value of the slope
What is the value of the y-intercept
NOTE: Round answers to three decimal laces
Problem 2
Problem 2
Explained and unexplained variation and the least-squares regression line
Given the following data:
x y
107.4 125.7
122.1 131.9
127.4 123.1
137 145.6
147.7 141.6
What is the equation for this sample?
What is the variation in the sample y values that is not explained by the estimated linear relationship (SSE)?
What is the proportion of the toal variation in the sample y values that is explained by the estimated linear relationship (r-squared)?
For the data point (107.4,125.7) what is the residual?
Problem 3
Problem 3
Linear relationship and the sample co
elation coefficient
Given the following four data sets and scatter plots.
x y u v
1 3.4 1 10
2 5.8 2 9
3 8.2 3 8
4 9.2 4 7
5 9.5 5 6
6 10.1 6 5
7 9.2 7 4
8 7.8 8 3
9 6.3 9 2
10 4.1 10 1
w t m n
1 7.6 1 3
2 9 2 4.1
3 7.3 3 3.6
4 5.6 4 5.3
5 8.4 5 5
6 4.7 6 7.2
7 5 7 6.3
8 6.7 8 7.8
9 5.9 9 7.2
10 3.9 10 7.9
Answer the following questions: (by giving the 2 variables or the answer None)
Which data set is there evidence of a strong nonlinear relationship between 2 variables?
Which data set indicates the strongest negatibe linear relationship between 2 variables?
Which data set has an apparent positive, but not perfect, linear relationship between 2 variables?
Which data set indicates a perfect positive linear relationship between 2 variables?
1 2 3 4 5 6 7 8 9 10 3.4 5.8 XXXXXXXXXX XXXXXXXXXX 9.5 10.1 XXXXXXXXXX 7.8 6.3 XXXXXXXXXX 1 2 3 4 5 6 7 8 9 10 10 9 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 10 7.6 9 7.3 5.6 8.4 4.7 5 6.7 5.9 3.9 1 2 3 4 5 6 7 8 9 10 3 XXXXXXXXXX 3.6 5.3 5 7.2 6.3 7.8 7.2 7.9
Problem 4
Problem 4
Regression 2 Independent Variables
Predicting job performance of auto mechanics based on mechanical aptitude test scores and personality testing that measures conscientiousness.
Given the following data
Y = job performance
X1 = mechanical aptitude scores
X2 = persomality test/conscientiousness measure
Y X1 X2
1 1 40 25
2 2 45 20
3 1 38 30
4 3 50 30
5 2 48 28
6 3 55 30
7 3 53 34
8 4 55 36
9 4 58 32
10 3 40 34
11 5 55 38
12 3 48 28
13 3 45 30
14 2 55 36
15 4 60 34
16 5 60 38
17 5 60 42
18 5 65 38
19 4 50 34
20 3 58 38
What is the regression equation with the 2 idependent variables (x1, x2)?
What is the co
elation coefficient?