Question

A.) This is a small set of data provided to investigate the relationship between the age of a lab computer and the number of service calls on it for the school year. Computer output for these data follows.

The following data was reported

X Age of lab computer    1 1 2 2 2 3 3 3 3 4 5 5

Y Number of repair calls 1 0 2 0 3 1 3 2 5 3 5 4

The regression equation is

rep call = - 0.297 + 0.958 age

Predictor      Coef      SE Coef       T            P

Constant    -0.2966    0.8553       -0.35      0.736

age             0.9576    0.2751         3.48     0.006

S = 1.21989     R-Sq = 54.8%     R-Sq(adj) = 50.3%

Analysis of Variance

Source              DF        SS        MS         F          P

Regression          1       18.035   18.035   12.12    0.006

Residual Error    10      14.881    1.488

Total                   11      32.917

What is the coefficient of determination for this relationship?

a.) 1.219

b.) 54.8%

c.) 50.3%

B.) Using the computer output above, test whether there is a statistically significant linearrelationship between X and Y. Use a level of significance of .05. Make a decision for the test and state your decision rule.

a.) Reject the null hypothesis because .006 < .05

b.) Fail to reject the null hypothesis because .006 > .011

c.) Fail to reject the null hypothesis because .006 < .05

C.) Explain what the 95% C.I. (Computer output below) for x=3 means.

Obs    Fit    SE Fit         95% CI        95% PI

1     2.576    0.355    (1.785, 3.368) (-0.255, 5.407)

a.) 95% C.I. for the number of service calls for computers that are 3 years old

b.) 95% C.I. for the mean number of service calls for computers that are 3 years old

c.) 95% C.I for the number of service calls for one particular 3 year old computer

D.) Explain what the 95% P.I. (Computer output below) for x=3 means.

Obs    Fit    SE Fit         95% CI        95% PI

1     2.576    0.355    (1.785, 3.368) (-0.255, 5.407)

a.) 95% C.I for the number of service calls for one particular 3 year old computer

b.) 95% C.I. for the number of service calls for computers that are 3 years old

c.) 95% C.I. for the mean number of service calls for computers that are 3 years old

Answer 1

Ans.

A) We know that coefficient of determination i.e. R^2 = SSreg/SStot ; reg: regression and tot: Total

Therefore coefficient of determination (R^2)= 50.4% .

B) From the given output , we can see that the P-value of coefficient/ slope of age variable is 0.006 , therefore we have sufficient evidence to reject our null hypothesis i.e. there is a statistically significant relation between X and Y , at 5% level of significance .

Hence we reject the null hyothesis because 0.006<0.05.

1) From the regression output we get the regression equation as : -0.2966 +0.9576X = Y

Therefore for fited value= 2.576 ,we have X= 3.

A 95% PI (Prediction Interval) refers to the : 95% confidence interval for the number of service calls for computers that are 3 years old.