## Statistics- STAT200 Homework 11 Due 5 pm, Friday

STAT200 Homework 11 Due 5 pm, Friday, Nov 20,

2015

1.

The data below are concerned with the Leaning

Tower of Pisa. Engineers concerned about the towerâs stability have done

extensive studies of its increasing tilt. The table gives measurements for the

year 1975 to 1987 (coded as 75 â 87). The variable âleanâ represents the

difference between where a point on the tower would be if the tower were

straight and where it actually is. The data are coded as tenths of a millimeter

in excess of 2.9 meters, so that 1975 lean, which was 2.9642 meters, appears in

the table as 642. Only the last two digits of the year were entered into the

computer:

Year

75

76

77

78

79

80

81

82

83

Lean

642

644

656

667

673

688

696

698

713

Year

84

85

86

87

Lean

717

725

742

757

(a)

Plot the data. Does the trend in lean over time

appear to be linear?

(b)

What is the equation of the least âsquares line?

What percent of the variation in lean is explained by this line?

(c)

Give a 99% confidence interval for the average

rate of change (tenths of a millimeter per year) of the lean.

(d)

The engineers working on the Leaning Tower of

Pisa were most interested in how much the tower would lean if no corrective action

were taken. Use the least-squares equation to predict the towerâs lean in the

year 2000, coded as 100.(Note: The tower was renovated in 2001 to make sure it

does not fall down. )

(e)

What is the 95% prediction interval for the lean

in year 100? What is the 95% confidence interval for the mean response of the

lean then?

2.

In each of the following settings, give a 95%

confidence interval for the coefficient of x2.

(a)

n=26, Ŷ=1.6+6.4 x1+5.7 x2,

SE of b2=3.1

(b)

n=26, Ŷ=1.6+4.8 x1+3.2 x2+5.2

x3, SE of b2=2.2

(c, d) For each of the settings in (a),(b), test

the null hypothesis that the coefficient of x1 is zero versus the two-sides

alternative.

3.

A multiple regression analysis of 78 cases was

performed with 5 explanatory variables. Suppose that SSM=16.5 and SSE=100.8.

(a)

Find the value of the F statistics for testing

the null hypothesis that the coefficients of all the explanatory variables are

zero.

(b)

What are the degrees of freedom of this

statistic?

(c)

Find bounds on the P-value using Table. Show your

work.

4.

Letâs consider developing a model to predict

total score based on the peer review score (PEER), faculty-to-student ratio (FtoS),

and citations-to-faculty ratio (CtoF). Refer

to the attached dataset.

(a)

Generate scatterplots for each pair of the

variables. Do these relationships all look linear?

(b)

Compute the correlation between each pair of the variables.

Are certain explanatory variables more strongly associated with the total

score?

5.

For the same dataset for problem 4, considering a

regression model using all three explanatory variables.

(a)

Write out the statistical model for this

analysis, making sure to specify all assumptions.

(b)

Run the multiple regression model and specify the

fitted regression equation.

(c)

Generate a 95% confidence interval for each

coefficient.

(d)

What percent of the variation does this model

explain? What is the estimate for the standard deviation?

(e)

Is the regression model significantly better than

the intercept only model? Use the ANOVA F-test to test this idea.

**CLICK HERE TO ORDER A SIMILAR PAPER**

We pride ourselves in writing quality essaysCLICK HERE TO CONTACT US