CHAPTER 4 MULTIPLE CORRELATION AND REGRESSION
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IMPORTANT QUESTIONS
(Multiple Correlation and Regression)
1. From following information of variables X1, X2, and Y.
ΣX1 = 272, ΣX2 = 441, ΣY= 147, ΣX12= 7428, ΣX22=19461, ΣY
2 = 2173, ΣX1Y = 4013, ΣX1 X2 = 12005, ΣX2 Y
= 6485, n=10. Fit a regression equation Y on X1 and X2. Interpret the regression coefficients.
2. Suppose we are given following information with n=7, multiple regression model is y = 8.15 + 0.6X1 +
0.54X2 Here , Total sum of square = 1493, Sum of square due to error = 91 Find i) R2 and interpret it. ii)
Test the overall significance of model
3. It was reported somewhere that children whenever plays the game in computer, they used the
computer very roughly which may reduce the lifetime of computer. The random access memory (RAM)
of computer also plays a crucial role on the lifetime of a computer. A researcher wanted to examine how
the lifetime of a personal computer which is used by children is affected by the time (in hours) spends by
the children per day to play games and the available random access memory (RAM) measured in
megabytes (MB) of a used computer. The data is provided in the following table.
Lifetime (years): 5 1 7 2 3 4 6
Play time (hours/day): 2 8 1 5 6 3 2
RAM (in MB): 8 2 6 3 2 4 7
Identify which one is dependent variable? Solve this problem using multiple linear regression model and
provide problem specific interpretations based on the regression model developed.
4. A study was conducted among IT officers working in different IT Centers in Kathmandu valley, one of
the objectives of the study was to quantify the effect of age and working hour per day on Computer
Vision Syndrome (CVS). The CVS was measured in a continuum measurement scale varying from 0 to 50.
Few parts of the data were taken randomly from the surveyed data and provided in the following table
for statistical analysis.
Respondents ID 001 007 125 231 99 299 145
Scales of CVs 6 7 5 11 3 29 28
Age of respondents (in years) 24 26 30 41 47 50 52
Working hour (per day) 4 5 6 8 3 6 7
Recognize which one is dependent variable? Assuming that the relationship between CVS, age and
working hour is linear. Fit a multiple linear regression model to address the objective of the study and
interpret the model appropriately.
5. A computer manager is keenly interested to know how efficiency of her new computer program
depends on the size of incoming data and data structure. Efficiency will be measured by the number of
processed requests per hour. Data structure may be measured on how many tables were used to arrange
each data set. All the information was put together as follows.
Data Size (gigabytes) 6 7 7 8 10 10 15
Number of tables 4 20 20 10 10 2 1
Processed requests 40 55 50 41 17 26 16
Identify which one is dependent variable? Fit the appropriate multiple regression model and provide
problem specific interpretations of the fitted regression coefficients.
6.For trivariate distribution r12=0.4, r23=0.5 and r13=0.6. Find (I)R1.23 (II)r23.1 (iii)R1.232
(iv) r23.12
and comment.
7. Suppose you are given following information;
Multiple regression model y=5+18 X1 +20 X2,
sample Size n=28, total sum of squares (TSS)=250, Sum of square due to error (SSE)=100, standard error
of regression coefficient of X1(Sb1) =3.2 , Standard error of regression coefficient of X2 (Sb2=5.5
Test the significance of regression coefficient of X1 at 1% level of significance. Also test the over all
significance of regression coefficients at 5% level of significace.
8. Write short notes on
a. Adjusted R2
b. Multiple correlation
c.Multiple Linear Regression (MLR)