Question 1: A doctor wanted to determine whether there is a relation between a male's age and his HDL (so-called good) cholesterol.
The doctor randomly selected 17 of his patients and determined their HDL cholesterol. The data obtained by the doctor is the in the data table below. Complete parts (a) through (d) below.
(a) Draw a scatter diagram of the data, treating age as the explanatory variable. What type of relation, if any, appears to exist between age and HDL cholesterol?
A. The relation appears to be nonlinear.
B. There does not appear to be a relation.
C. The relation appears to be linear.
(b) Determine the least-squares regression equation from the sample data.
(c) Are the any outliers or influential observations,
(d) Assuming the residuals are normally distributed, test whether a linear relation exists between age HDL cholesterol levels at the α = 0.01 level of significance.
What are the null and alternative hypotheses?
A. H0: β1 = 0; H1: β1 ≠ 0;
B. H0: β1 = 0; H1: β1 < 0;
C. H0: β1 = 0; H1: β1 > 0;
Use technology to compute the P-value. Use the Help button for further assistance.
P-value is __.
(Round to three decimal places as needed.)
Question 2:
Suppose a multiple regression model is given by y^ = - 3.92x1 + 7.79x2 + 24.51. What would an interpretation of the coefficient of x1 be? Fill in the blank below.
An interpretation of the coefficient of x1 would be, "if x1 increases by 1 unit, then the response variable will decrease by __ units, on average, while holding x2 constant."
Question 3:
Determine if there is a linear relation among air temperature x1, wind speed x2, and wind chill y. The following data show the measured values for various days.
|
x1
|
20
|
-30
|
-20
|
30
|
30
|
30
|
-10
|
-20
|
-30
|
0
|
0
|
10
|
-30
|
-10
|
|
x2
|
90
|
70
|
30
|
50
|
20
|
30
|
20
|
40
|
50
|
10
|
40
|
80
|
100
|
50
|
|
y
|
-32
|
-96
|
-64
|
-8
|
6
|
0
|
-44
|
-70
|
-88
|
-22
|
-44
|
-44
|
-104
|
-62
|
(a) Find the least squares regression equation y^ = b0 + b1x1 + b2x2, where x1 is air temperature and x2 is wind speed, and y is the response variable, wind chill. y^ = __ + __ x1 + x2 (Round to three decimal places as needed.)