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1.Write short notes on
a. Correlation
b. Regression
c. Spearman Rank Correlation Coefficient
d. Coefficient of determination
2. In a certain type of metal test specimen. the effect of normal stress on a specimen is known to be
functionally related to shear resistance. The following table gives the data on the two variables.
Normal stress 26 25 28 23 27 23 24 28 26
Shear resistance 22 27 24 27 23 25 26 22 21
(i) Identify which one is response variable, and fit a simple regression line, assuming that the relationship
between them is linear.
(ii)Interpret the regression coefficient with reference to your problem.
(iii) Obtain the coefficient of determination, and interpret this.
(iv) Based on the fitted model in (i), predict the shear resistance for normal stress of 30 kilogram per
square centimeter .
3. As part of the study of the psychobiological correlates of success in athletes, the following
measurements are obtained from members of Nepal national football team.
Anger 6 7 5 21 13 5 13 14
Vigor 30 23 29 22 19 19 28 19
Calculate Spearman's rank correlation coefficient.
4. A study was done to study the effect of ambient temperature on the electric power consumed by a
chemical plant. Following table gives the data which are collected from an experimental pilot plant.
Temperature (0F). 27 45 72 58 31 60 34 74
Electric Power ( BTU) 250 285 320 295 265 298 267 321
(i) Identify which one is response variable, and fit a simple regression line, assuming that the relationship
between them is linear.
(ii) Interpret the regression coefficient with reference to your problem.
(iii) Obtain coefficient of determination, and interpret this.
(iv) Based on the fitted model in (i), predict the power consumption for an ambient temperature of
650F.
5. Following data represent the preference of 10 students studying B.Sc.(CSIT) towards two brands of
computers namely DELL and HP.
Computer Student preference
Lenovo 5 2 9 8 1 10 3 4 6 7
Acer 10 5 1 3 8 6 2 7 9 4
Apply appropriate statistical tool to measure whether the brand preference is correlated. Also interpret
your result.
6. Write the properties of correlation coefficient. The time it takes to transmit a file always depends on
the file size. Suppose you transmitted 30 files, with the average size of 126K bytes and the standard
deviation of 35 Kbytes. The average transmitted time was 0.04 seconds with the standard deviation 0.01
seconds. The correlation coefficient between the time and size was 0.86. Based on these data, fit a linear
regression model and predict the time it will take to transmit a 400K byte file.
7. Calculate Spearman's rank correlation coefficient for the following ranks given by three judges in a
music contest.
1st Judge 2 1 4 6 5 8 9 10 7 3
2nd Judge 4 3 2 5 1 6 8 9 10 7
3rd Judge 5 8 4 7 10 2 1 6 9 3
Indicate which pair of judges has the nearest approach to music.
8. For 10 observations on two variables X and Y the following information are as follows: ∑X=666,
∑Y=663, ∑X2=44490, ∑Y2=44061, ∑XY=44224 . Compute Karl Pearsons coefficient of
correlation.
9.From 20 pairs of X and Y variables the following results obtained ∑X=127, ∑Y=100, ∑X2=860
, ∑Y2=549, ∑XY=674 at the time of verification , the following wrong values of X and Y were
taken as X=10,8 and Y=14,6 instead of correct values X=8,6 and Y=12,8. Find correct value of
correlation.
10.Calculate the correlation coefficient between sales and repair of computers as given below:
sales 50 55 55 60 65 70 65 60
Repair 11 13 14 16 16 15 15 20
11. Find the regression line of sons height on father height.
Father: 67 63 66 71 69 65 62 70 61 72
Son: 68 66 65 70 67 67 64 71 62 63
Also estimate the height of son for the given height of father as 70 inches. Also determine coefficient of
determination and interpret.
12Calculate correlation coefficient between X and Y
X 6 2 10 4 8
y 9 11 5 8 7
13. Find the regression equation X on Y from the following data.
X 5 15 20 25 30
Y 50 60 80 110 130
14.National planning commission is performing preliminary study to determine the relationship between
certain economic indicator and annual percentage change in gross national product (GNP) . The concern
is to estimate the percentage change in GNP. One of such indicator being estimated is governments
deficit. Data on 6 years are given below ;
Percentage change in GNP 3 1 4 1 2 3
Government deficit in lakh Rs 50 200 70 100 90 40
a. Develop the estimating equation to predict percentage change in GNP for government deficit.
b. Interpret the estimated regression coefficient.
c. What percentage change in GNP would be expected in a year in which government deficit was Rs 110
lakh.
d. Compute the coefficient of determination and interpret.
15.A computer manager interested to know how efficiency of his / her new computer program which
depends on the size of incoming data . Efficiency will be measured by the number of processed requests
per hour. In general , larger data sets require more computer time and therefore, fewer requests are
processed within 1 hour. Applying the program to data sets of different sizes, the following data were
generated.
Data Size ( gigabytes) 6 7 7 8 10 10 15
Processed requests 40 55 50 41 17 26 16
a. Identify which one response variable and fit a simple regression line assuming that the relationship is
linear.
b. Interpret the regression coefficient with reference to your problem.
c. obtain the coefficient of determination and interpret this.
d. Based on the fitted model predict the efficiency of new computer for data size 12 ( gigabytes ). Does it
possible to predict efficiency for data size of 30 ( gigabytes)?
16.A city council has gathered data on number of minor traffic accidents and the number of youth
football games that occurred in town over the weekends.
X ( football games) 20 30 10 12 15 25 34
Y ( minor accidents) 6 9 4 5 7 8 9
(a)Developed the regression equation to predict minor accidents from football games.
(b)Predict the number of minor traffic accidents that will occur at weekends during which X=30.
(c)Calculate the value of coefficient of determination.
(d)Calculate the value of standard error of estimate.