Question

REGRESSION. The length of a species of fish is to be represented as a function of the age (measured in days) and water temperature (degrees Celsius). The fish are kept in tanks at 25, 27, 29 and 31 degrees Celsius. After birth, a test specimen is chosen at random every 14 days and its length measured. The dataset is presented below. What is the estimated regression equation?

	Age	Temp	Length
1	14	25	620
2	28	25	1,315
3	41	25	2,120
4	55	25	2,600
5	69	25	3,110
6	83	25	3,535
7	97	25	3,935
8	111	25	4,465
9	125	25	4,530
10	139	25	4,570
11	153	25	4,600
12	14	27	625
13	28	27	1,215
14	41	27	2,110
15	55	27	2,805
16	69	27	3,255
17	83	27	4,015
18	97	27	4,315
19	111	27	4,495
20	125	27	4,535
21	139	27	4,600
22	153	27	4,600
23	14	29	590
24	28	29	1,305
25	41	29	2,140
26	55	29	2,890
27	69	29	3,920
28	83	29	3,920
29	97	29	4,515
30	111	29	4,520
31	125	29	4,525
32	139	29	4,565
33	153	29	4,566
34	14	31	590
35	28	31	1,205
36	41	31	1,915
37	55	31	2,140
38	69	31	2,710
39	83	31	3,020
40	97	31	3,030
41	111	31	3,040
42	125	31	3,180
43	139	31	3,257
44	153	31	3,214

		Y = B0 + B1X1 + B2X2 + e
		E(Y) = B0 + B1X1 + B2X2
		Y-hat = 3904.27 + 26.24X1 - 106.414X2
		None of the above

Part 2

1.       REGRESSION. Which variable is the response variable?

		Age
		Water temperature
		Length of fish *
		Not defined

Part 3

1.       REGRESSION. Is there evidence of collinearity between the independent variables?

		Yes, temperature and length are collinear in that their correlation is quite high
		Yes, temperature and age of fish are collinear
		No, temperature and age have no correlation
		No, temperature and length have a low correlation
		Yes, Age and length have a high correlation
		None of the above

Part 4

1.       REGRESSION. What proportion of the variation in the response variable is explained by the regression?

		About 90 percent
		About 81 percent
		About 85 percent
		None of the above

Part 5

1.       REGRESSION. The F statistic indicates that:

		The regression, as a whole, is statistically significant
		More than half of the variation in Y is explained by the regression
		Age of fish is an important explanatory variable in the model
		Length of fish is an important explanatory variable in the model
		Water temperature is an important explanatory variable in the model
		None of the above

Part 6

1.       REGRESSION. The t-test of significance indicates that:

		The regression, as a whole, is statistically significant
		More than half of the variation in Y is explained by the regression
		Age of fish contributes information in the prediction of length of fish
		Length of fish contributes information in the prediction of age of fish
		Length of fish contributes information in the prediction of temperature

Part 7

1.       REGRESSION. The t-test of significance indicates that (same question but choose the correct answer):

		The regression, as a whole, is statistically significant
		More than half of the variation in Y is explained by the regression
		Length of fish is an important explanatory variable in the model
		Water temperature is an important explanatory variable in the model
		None of the above

Part 8

1.       REGRESSION. Assuming you ran the regression correctly, plot the residuals (against Y-hat). The plot shows that:

		The residuals appear to curve downwards, like a bowl facing down
		The residuals appear to curve upwards, like a bowl facing up (V shape)
		The residuals appear to be fanning out and are mostly spread out at the end
		The residuals appear random
		None of the above

Part 9

1.       REGRESSION. Which of the following types of transformation may be appropriate given the shape of the residual plot?

		Logarithmic transformation in both Y and the X variables
		Quadratic transformation to correct for curvilinear relationship
		No transformation is necessary

Part 10

1.       REGRESSION. This type of dataset is best described as a ____ and a residual problem common with this type of data is ___

		Cross-sectional data; heteroscedasticity
		Time series data; heteroscedasticity
		Cross-sectional data; residual correlation
		Time series data; residual correlation
		Cross-sectional data; multicollinearity
		None of the above

Answer 1