Probability and Statistics for Engineering and the Sciences
9th Edition
ISBN: 9781305251809
Author: Jay L. Devore
Publisher: Cengage Learning
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Chapter 12.3, Problem 32E
Exercise 16 of Section 12.2 gave data on x = rainfall volume and y = runoff volume (both in m3). Use the accompanying Minitab output to decide whether there is a useful linear relationship between rainfall and runoff, and then calculate a confidence interval for the true average change in runoff volume associated with a 1 m3 increase in rainfall volume.
The regression equation is
runoff = −1.13 + 0.827 rainfall
| Predictor | Coef | Stdev | t-ratio | P |
| Constant | −1.128 | 2.368 | −0.48 | 0.642 |
| rainfall | 0.82697 | 0.03652 | 22.64 | 0.000 |
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A researcher interested in explaining the level of foreign reserves for the country of Barbados
estimated the following multiple regression model using yearly data spanning the period 2001 to
2016:
FR=a+B01L+YEXP+8FDI
Where FR = yearly foreign reserves (So000's), OIL = annual oil prices, EXP = yearly total exports
(S000's) and FDI = annual foreign direct investment ($000's). The sample of data was processed
using MINITAB and the following is an extract of the output obtained:
Predictor
Coef
StDev
t-ratio
p-value
Constant 5491.38 2508.81
2.1888
0.0491
OIL
85.39
18.46
4.626
0.0006
EXP
-377.08
112.19
0.0057
FDI
-396.99
160.66
-2.471
s - 2.45
R-sq = 96.3%
R-sq(adj) = 95.3%
Analysis of Variance
Source
DF
MS
F
Regression
3
1991.31 663.77
??
Error
12
43. רר
6.45
Total
15
a) What is dependent and independent variables?
b) Fully write out the regression equation
c) Fill in the missing values **', **', '?'and *??"
A researcher interested in explaining the level of foreign reserves for the country of Barbados
estimated the following multiple regression model using yearly data spanning the period 2001 to
2016:
FR=a+B0IL+YEXP+8FDI
Where FR = yearly foreign reserves ($000°s), OIL = annual oil prices, EXP = yearly total exports
($000's) and FDI = annual foreign direct investment ($000`s). The sample of data was processed
using MINITAB and the following is an extract of the output obtained:
Predictor
Coef
StDev
t-ratio
p-value
Constant
5491.38
2508.81
2.1888
0.0491
OIL
85.39
18.46
4.626
0.0006
EXP
-377.08
112.19
0.0057
FDI
-396.99
160.66
-2.471
**
s = 2.45
R-sq = 96.3%
R-sq (adj)
= 95.3%
Analysis of Variance
Source
DF
MS
F
Regression
1991.31
663.77
??
Error
12
77.4
6.45
Total
15
c) Fill in the missing values
?'and ??
Nine data points of data yield
r=0.867
and the regression equation
y=19.4+0.93x.
Also,
y=64.7.
What is the best predicted value of y for
x=40?
Chapter 12 Solutions
Probability and Statistics for Engineering and the Sciences
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- Does Table 1 represent a linear function? If so, finda linear equation that models the data.arrow_forwardA researcher interested in explaining the level of foreign reserves for the country of Barbados estimated the following multiple regression model using yearly data spanning the period 2001 to 2016: FR=a+B0IL+YEXP+8FDI Where FR = yearly foreign reserves ($000°s), OIL = annual oil prices, EXP = yearly total exports ($000's) and FDI = annual foreign direct investment ($000`s). The sample of data was processed using MINITAB and the following is an extract of the output obtained: Predictor Coef StDev t-ratio p-value Constant 5491.38 2508.81 2.1888 0.0491 OIL 85.39 18.46 4.626 0.0006 EXP -377.08 112.19 0.0057 FDI -396.99 160.66 -2.471 ** s = 2.45 R-sq = 96.3% R-sq (adj) = 95.3% Analysis of Variance Source DF MS F Regression 1991.31 663.77 ?? Error 12 77.4 6.45 Total 15 d) Hence test whether ß is significant. Give reasons for your answer. e) Perform the F Test making sure to state the null and alternative hypothesis. f) Given an interpretation of the term “R-sq“ and comment on its value.arrow_forwardA researcher interested in explaining the level of foreign reserves for the country of Barbados estimated the following multiple regression model using yearly data spanning the period 2001 to 2016: FR=a+BOIL+yEXP+8FDI Where FR = yearly foreign reserves ($000's), OIL = annual oil prices, EXP = yearly total exports ($000's) and FDI = annual foreign direct investment ($000's). The sample of data was processed using MINITAB and the following is an extract of the output obtained: Predictor Сoef StDev t-ratio p-value Constant 5491.38 2508.81 2.1888 0.0491 OIL 85.39 18.46 4.626 0.0006 EXP -377.08 112.19 0.0057 FDI -396.99 160.66 -2.471 ** S = 2.45 R-sq 96.3% R-sq (adj) 95.3% Analysis of Variance Source DF MS F Regression 1991.31 663.77 ?? Error 12 77.4 6.45 Total 15 a) What is dependent and independent variables? b) Fully write out the regression equation c) Fill in the missing values *', ***', '?'and ??' d) Hence test whether B is significant. Give reasons for your answer. e) Perform the F…arrow_forward
- A researcher interested in explaining the level of foreign reserves for the country of Barbados estimated the following multiple regression model using yearly data spanning the period 2001 to 2016: FR=a+B0IL+YEXP+8FDI Where FR = yearly foreign reserves ($000°s), OIL = annual oil prices, EXP = yearly total exports ($000's) and FDI = annual foreign direct investment ($000`s). The sample of data was processed using MINITAB and the following is an extract of the output obtained: Predictor Coef StDev t-ratio p-value Constant 5491.38 2508.81 2.1888 0.0491 OIL 85.39 18.46 4.626 0.0006 EXP -377.08 112.19 0.0057 FDI -396.99 160.66 -2.471 ** s = 2.45 R-sq = 96.3% R-sq (adj) = 95.3% Analysis of Variance Source DF MS F Regression 1991.31 663.77 ?? Error 12 77.4 6.45 Total 15 a) What is dependent and independent variables? b) Fully write out the regression equationarrow_forwardA researcher interested in explaining the level of foreign reserves for the country of Barbados estimated the following multiple regression model using yearly data spanning the period 2001 to 2016: FR=a+BOIL+YEXP+8FDI Where FR = yearly foreign reserves ($000's), OIL = annual oil prices, EXP = yearly total exports (S000's) and FDI = annual foreign direct investment (S000's). The sample of data was processed using MINITAB and the following is an extract of the output obtained: Predictor Coef StDev t-ratio p-value Constant 5491.38 2508.81 2.1888 0.0491 OIL 85.39 18.46 4.626 0.0006 ЕXP -377.08 112.19 0.0057 FDI -396.99 160.66 -2.471 ** s = 2.45 R-sq = 96.3% R-sq (adj) = 95.3% Analysis of Variance Source DF MS Regression 1991.31 663.77 ?? Error 12 77.4 6.45 Total 15arrow_forwardA researcher interested in explaining the level of foreign reserves for the country of Barbados estimated the following multiple regression model using yearly data spanning the period 2001 to 2016: FR=a+BOIL+YEXP+8FDI Where FR = yearly foreign reserves (S000's), OIL = annual oil prices, EXP = yearly total exports ($000's) and FDI = annual foreign direct investment ($000°s). The sample of data was processed using MINITAB and the following is an extract of the output obtained: Predictor Coef StDev t-ratio p-value Constant 5491.38 2508.81 2.1888 0.0491 OIL 85.39 18.46 4.626 0.0006 ЕXP -377.08 112.19 0.0057 FDI -396.99 160.66 -2.471 S = 2.45 R-sq = 96.3% R-sq (adj) = 95.3% Analysis of Variance Source DF MS F Regression 3 1991.31 663.77 ?? Error 12 77.4 6.45 Total 15arrow_forward
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- estimated the following multiple regression model using yearly data spanning the period 2001 to Where FR = yearly foreign reserves ($000's), OIL = annual oil prices, EXP = yearly total exports ($000's) and FDI = annual foreign direct investment ($000's). The sample of data was processed A researcher interested in explaining the level of foreign reserves for the country of Barbados 2016: FR=a+B0IL+YEXP+8FDI using MINITAB and the following is an extract of the output oblamed. Predictor Coef StDev p-value t-ratio 5491.38 2508.81 2.1888 Constant 0.0491 OIL 85.39 18.46 4.626 0.0006 EXP -377.08 112.19 0.0057 FDI -396.99 160.66 -2.471 S = 2.45 R-sq = 96.3% R-sq (adj) = 95.3% Analysis of Variance Source MS F DF Regression 3 1991.31 663.77 ?? Error 12 77.4 6.45 Total 15 a) What is dependent and independent variables? b) Fully write out the regression equation c) Fill in the missing values *', **', ?'and ??' d) Hence test whether B is significant. Give reasons for your answer. e) Perform the F…arrow_forwardThe estimated regression equation for a model involving two independent variables and 10 observations follows. Y=25.7067 + 0.2795x1 + 0.7337x2 A. Interpret b1 and b2 in this estimated trgression equation. B1 = ? B2 = ? Thank youarrow_forwardestimated the following multiple regression model using yearly data spanning the period 2001 to Where FR = yearly foreign reserves ($000's), OIL = annual oil prices, EXP = yearly total exports ($000's) and FDI = annual foreign direct investment ($000's). The sample of data was processed A researcher interested in explaining the level of foreign reserves for the country of Barbados 2016: FR=a+B0IL+YEXP+8FDI using MINITAB and the following is an extract of the output oblamed. Predictor Coef StDev p-value t-ratio 5491.38 2508.81 2.1888 Constant 0.0491 OIL 85.39 18.46 4.626 0.0006 EXP -377.08 112.19 0.0057 FDI -396.99 160.66 -2.471 S = 2.45 R-sq = 96.3% R-sq (adj) = 95.3% Analysis of Variance Source DF S MS F Regression 663.77 ?? 3 1991.31 Error 12 77.4 6.45 Total 15 d) Hence test whether B is significant. Give reasons for your answer. e) Perform the F Test making sure to state the null and alternative hypothesis. f) Given an interpretation of the term "R-sq" and comment on its value.arrow_forward
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