Fundamentals of Biostatistics
8th Edition
ISBN: 9781305268920
Author: Bernard Rosner
Publisher: Cengage Learning
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The following table shows the starting salary and profile of a sample of 10
employees in a certain call center agency. Run a multiple regression
analysis with starting salary as the dependent variable (pesos) and GPA,
years of experience and civil service ratings as the independent variables.
Use .05 level of significance.Which of the given independent variables
is/are significant? *
avil
Years of
Starting salary GPA
service
experience
ratings
79.5
15000 80.1
15000 81.2
1
1
78.0
15500 81.3
16000 82.4
2
3
79.0
80.0
85.0
16200 83.4
3
17500 87.9
89.9
89.1
84.1
89.0
89.2
4
18000 90.3
5
16,300 84.2
3
17000 87.0
4
17900 88.1
GPA and years of experience
GPA, years of experience and civil service ratings
intercept, GPA, years of experience and civil service ratings
O years of experience and civil service ratings
Suppose researchers are interested in exploring the factors which affect depression for Australian adults. The researchers recruited a sample of 99 Australian adults and collected data on several variables which may influence depression. Note that here depression is represented by a score, with higher values representing higher levels of depression.
The variables for this study are listed below:
Age
Gender (0 = female, 1 = male)
Stress level
Anxiety level
Depression
Prior to running their analysis (multiple regression), the researchers would like to check the regression assumptions for the data. Which of the assumptions below is not an assumption for multiple regression?
A) Sphericity
B) Linearity and Additivity
C) Equal variances
D) Normality
E) Metric scales
Both arm circumference and BMI measurements have been used as screening tools for being underweight, overweight, or obese. We want to determine if there is a significant correlation between arm circumference (in centimeters or cm) and body mass index or BMI (in kg.m2) among 10 participants. The results of a correlation and regression analysis are indicated in the Excel output below. The mean arm circumference (the independent variable) was 35.2 cm, and the mean BMI (the dependent variable) was 30.7 kg.m2.
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.855646
R Square
0.732129
Adjusted R Square
0.698646
Standard Error
3.806088
Observations
10
ANOVA
df
SS
MS
F
Significance F
Regression
1
316.7456
316.7456
21.86518
0.001590054
Residual
8
115.8904
14.4863
Total
9
432.636…
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- Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4arrow_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: ??=?+????+????+???? 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 SS MS F p…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: ??=?+????+????+???? 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…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: ??=?+????+????+???? 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%…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: ??=?+????+????+???? 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 0.0491OIL 85.39 18.46 4.626 0.0006EXP -377.08 112.19 * 0.0057FDI -396.99 160.66 -2.471 ** S = 2.45 R-sq = 96.3% R-sq(adj) = 95.3% Analysis of VarianceSource DF SS…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: ??=?+????+????+???? 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 SS MS F p Regression 3 1991.31 663.77 ? ?? Error 12 77.4 6.45 Total 15 a). Fill in the missing values ‘*’, ‘**’,…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: ??=?+????+????+???? 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%…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: ??=?+????+????+???? 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 SS MS F p Regression 3 1991.31 663.77 ? ?? Error 12 77.4 6.45 Total 15 Fill in the missing values ‘*’, ‘**’, ‘?’and ‘??’…arrow_forward
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