Practice Problems for Midterm 1 - Applied Linear Regression | 22S 152, Exams of Statistics

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Name: _______________________________________

PRACTICE PROBLEMS for MIDTERM 1 in 2002

22S:152, Regression and Design

Fall 1999 Instructor: Cowles

Midterm 1

1. The graph below summarizes the distribution of life expectancies for males in 97countries of the world in 1992. Refer to it in answering the following questions.

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(a) What kind of plot is this?(b) Does the plot indicate that the distribution of values is skewed or symmetric? If

skewed, in which direction? (c) Are there any outliers?(d) If you needed to symmetrize the distribution of these values, which transforma-

tion from Tukey’s ladder of powers would you try first? Why?

2. The SAS output below is from the regression of live birth rate per 1000 population(“liverbirth”) on per capita gross domestic product (“pcgdp”) in 97 countries of theworld in 1992. Refer to it in answering the following questions.

Dependent Variable: livebrth

Parameter Estimates Parameter

Standard

Variable

DF^

Estimate

Error

t Value

Pr > |t|

Intercept

<.

pcgdp

-0.

0.

<.

Parameter Estimates

Variable

DF^

95% Confidence Limits

Intercept

pcgdp

-0.

-0.

(a) What are the estimates of the intercept and slope?(b) Interpret what the slope means for this particular application.(c) At the .01 significance level, is the slope significantly different from 0? How can

you tell? (d) What is the 95% confidence interval for the slope? Also, interpret what it means.(e) Based on the regression output, which of the following statements is true of the

sample correlation coefficient

r^ between

livebirth

and

pcgdp

?

i.^ r must be positive. ii.^ r

must be negative. iii.^ r^ must be exactly 0.

iv. Nothing can be concluded about

r^ from this output.

3. The plot below shows the regression of infant mortality rate on live birth rate for 97countries in the world in 1992.

95% confidence bands for

E(

Y^ |X

) are also plotted.

(a) Interpret what the confidence bands mean.(b) Does the fact that so few data points lie between the confidence bands indicate

that there is something wrong with the model? Why or why not?

4. The SAS output below is the ANOVA table for the regression of heart rate in beatsper minute on body temperature in degrees Fahrenheit for 130 healthy adults.^ Dependent Variable: HEART

Analysis of Variance Sum of

Mean

Source

DF^

Squares

Square

F Value

Prob>F

Model

0.

Error

C Total

Root MSE

R-square

0.

Dep Mean

Adj R-sq

0.

C.V.

(a) What proportion of the variability in heart rate is explained by the predictor

variable? (b) At the .01 significance level, is the slope significantly different from 0? How can

you tell? (c) What is the interpretation of the circled number?