Question

(Unscrambling time) A group of student asked a random sample of fifty Stern students and faculty to unscramble the six letter word. The sequence M-E-I-P-T-R was used for all fifty persons. The data included the following two variables: Time (in seconds)=the time it took a person to unscramble a word, Age=age of a person in years. Answer the following questions using Minitab output that follows the problem.

a) Is the estimated regression model of Time on Age statistically signif- icant at a= 0.05?

b) Find the p-value of the test that you carried out in a) and interpret it.

c) Interpret the coefficients in the estimated regression model.

d) Compute and interpret the sample coefficient of determination (r2) for this regression.

e) Construct a 90% confidence interval for the population coefficient of Age and interpret it.

f) Now suppose that you fitted the regression model in which Age is a response variable and Time is a predictor. What is the r2 of this new regression?

Regression Analysis: time (sec) versus age

Analysis of Variance

Source       DF     SS
Regression   1
Error.       48
Total.       49.   1055380

Model Summary

      S   R-sq
141.311

Coefficients

Term      Coef  SE Coef  T-Value  P-Value
Constant  23.7     60.8     0.39    0.698
age       4.86     2.21     2.20

Regression Equation
time (sec) = 23.7 + 4.86 age

Answer 1

a-b)

It can be test using t value for slope. Hypotheses are:

The test statistics is

t = 2.20

The degree of freedom:

df = 48

The p-value of t test is 0.0327.

Since p-value is less than 0.05 so we fail to reject the null hypothesis. That is we can conclude that the estimated regression model of Time on Age is statistically significant at a= 0.05.

c)

Slope = 4.86

That is for unit increase in age time is increased by 4.86 secs.

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Intercept = 23.7

If age is zero then time is 23.7 secs. It is meaningless in this case.

(d)

Need value of R-square or SSR to answer this question.

(e)

The critical value of t for 90% confidence interval and df=48 is 1.677. The confidence interval is

(f)

R-square will remain same.