Deck 11: Regression Analysis I

Question 1

The letter x usually represents the independent variable, also called predictor variable

Answer 1

True

Question 2

Consider the line y = -6 + 14x

A) What is its intercept?
B) What is its slope?

Answer 2

Part A: -6
Part B: 14

Question 3

The price y (in cents) of a domestic long distance telephone call is given by
y = 2x + 25
where x denotes the number of minutes that the call lasts.

A) What is the price, in dollars, of a 33 minutes call?
B) If the telephone company charged you $3.33 for a domestic long distance call, how long was that call?

Answer 3

Part A: $0.91
Part B: 154 minutes

Question 4

Identify the values of the parameters A) β₀, B) β , and C) δ in the statistical model
Y = -14 + 15 x + e
where e is a normal random variable with mean 0 and standard deviation 7.

Question 5

Under the linear regression model, determine the (A) mean and (B) standard deviation of Y, for x = 12, when β₀ = 6, β₁ = 5, and δ = 7.

Question 6

Consider the following linear regression model
Y = β₀ + β₁x + e
where β₀ = 4, β₁ = -2, and the normal random variable e, has the standard deviation 3.

A) What is the mean of the response Y when x = 8?
B) Will the response at x = 9 always be larger than that at x = 8? Answer "Yes" or "No".

Question 7

Data on the number of cans of beverage served, y , and the number of students, x, attending a TV watching party were recorded on six occassions

A) Calculate $\bar{x}$
B) Calculate $\bar{y}$
C) Calculate S_xx
D) Calculate S_yy
E) Calculate S_xy
Calculate the least squares estimate
G) Calculate the least squares estimate

Question 8

Data on the number of cans of beverage served, y , and the number of students, x, attending a TV watching party were recorded on six occassions
Find the value of . Round your answer to three decimal places.

A) .6
B) -1.4
C) .4
D) .7

Question 9

A basketball fan collected data on the number of points per game, y, of her favorite player, associated with the number of minutes, x, played per game
Given that
S_xx = 189.50, S_xy 317.50, and S_yy 581.50, calculate the residual sum of squares S.S.E.

Question 10

Consider the following data set

A) Determine the fitted line
B) Use the fitted line to predict the value of y when x = 3.5.

Question 11

Which of the following statements is (are) true?

III) The point ( $\bar{x}$ , $\bar{y}$ ) lies on the fitted regression line

A) Only I and II
B) Only I and III
C) Only II and III
D) All of them

Question 12

Suppose that n = 21, $\bar{x}$ = 38.044, $\bar{y}$ = 89.27, S_xx = 994.045, S_xy = 6191.08, and S_yy = 76,293.5.

A) Obtain the equation of the best fitting straight line.
B) Calculate the residual sum of squares.
C) Estimate .

Round your answers to three decimal places.

Question 13

Temperature anomaly means a departure from a reference value, usually obtained by a long-term average. A positive anomaly indicates that the observed temperature was warmer than the reference value. The following table shows the annual anomalies for the highest temperatures in six recent decades..

A) Obtain the last squares fit of year to the predictor temperature anomaly.
B) Calculate the residual sum of squares.
C) Estimate .

Round your answers to three decimal places.

Question 14

Consider the following data.

A) Calculate the least squares estimate .

B) Calculate the least squares estimate .

C) Estimate the error variance .

D) Test H₀: $\beta$ ₁ = 0 versus H₁: $\beta$ ₁ $\neq$ 0 with $\alpha$ = 0.05. Answer "H₀ is rejected at $\alpha$ = 0.05" or "H₀ is not rejected at $\alpha$ = 0.05".
E) Estimate the expected y value corresponding to x = 3.
F) Give a 90% confidence interval for the expected y value at x = 3. Round your answer to two decimal places.

Question 15

Consider the following data set.
where S_xx = 10, S_xy = 16, and S_yy = 26.8. Construct a 95% confidence interval for $\beta$ ₁ . Round your answer to two decimal places.

Question 16

Consider the following data set:

where S_xx = 10 , S_xy = 25, and S_yy = 74.Construct a 90% confidence interval for the intercept $\beta$ ₀. Round your answer to three decimal places.

Question 17

The Human Development Index (H.D.I.) provides a composite measure of three dimensions of human development: life expectancy, adult literacy, and income. One county's H.D.I. trend is shown below.

A) Determine the equation of the least squares regression line.
B) Estimate the H.D.I. in year 6.5.
C) Construct a 95% confidence interval for the response in part B. Round your answer to three decimal places.

Question 18

Data are recorded at one ACM on the total time to wait in line and then complete a transaction y(minutes) and the number of persons, x, already in line.

A) Determine the equation of the least squares regression line. Round your answer to three decimal places.
B) Estimate the time to finish your transaction when 6 people are ahead of you. Round your answer to three decimal places.
C) Give a 95% prediction interval for the time to finish your transaction when 6 people are ahead of you in line. Round your answer to two decimal places.

Question 19

A recent graduate moving to a new job, collected a sample of rent (dollars) and size (square feet) of 2-bedroom apartments in a desirable area of the city. The data
have the summary statistics
We randomly selected 12 countries, of about 200 countries on the list. H.D.I. is the response variable y, and total fertility rate (births per woman), x, is the predictor variable. The data have the summary statistics.
n = 8 $\bar{x}$ = 1072.25 $\bar{y}$ = 1421.25 S_xx = 230081.5 S_yy = 217237.5
S_xy = 212376.5
Determine the equation of the best fitting straight line. Round your answer to three decimal places.

Question 20

One measure of the development of a country is the Human Development Index (H.D.I.) which combines life expectancy, literacy, and gross domestic product per capita into an index whose values lie between 0 and 1, inclusive.

We randomly selected 12 countries, of the 182 countries on the list. H.D.I. is the response variable y, and total fertility rate (births per woman), x, is the predictor variable. The data have the summary statistics.

n = 12 $\bar{x}$ = 1.825 $\bar{y}$ = .85 S_xx = 2.7625 S_yy = .0342 S_xy = -.1838

A) Estimate the mean value of H.D.I. for the total fertility rate of 2.5.
B) Construct a 95% confidence interval for the response in part A.
Round your answer to three decimal places.

Question 21

An advertising company collected data on the number of new contracts signed, y, and the number of presentations, x, made in each of six months. The summary statistics are
n = 6 $\bar{x}$ = 34 $\bar{y}$ = 7.1 S_xx = 1750 S_xy = 36.45 S_yy = .78
Determine the proportion of variation in y that is explained by linear regression. Round your answer to three decimal places.

Question 22

The total number of hours worked by a student, y, last week depends on the number of days, x, they worked. Data on twenty-eight students produce the summary statistics
n = 28 $\bar{x}$ = 3.21 $\bar{y}$ = 14.79 S_xx = 2260.714 S_xy = 1969.286 S_yy = 2076.714
Determine the proportion of variation in y that is explained by linear regression. Round your answer to three decimal places.

Question 23

Consider the following information:
n = 19 $\bar{x}$ = 9.959 $\bar{y}$ = 0.6679 S_xx = 1173.45 S_xy = 20.480 S_yy = 0.41771

A) If x is the predictor variable, determine the proportion of variation in y, that is explained by linear regression.
B) If y is the predictor variable, determine the proportion of variation in x, that is explained by linear regression.
Round your answers to three decimal places.

Question 24

Calculate the correlation coefficient between the number of grocery carts, x, ahead in line and the time, y, to complete checkout.

Question 25

Consider the data set
Calculate the
(a) sample means
(b) S_xx , S_xy , S_yy
(c) Calculate the least squares estimates β1 and β0.
(d) Calculate the sample correlation coefficient.

Question 26

Consider the data set



Calculate the
(a) sample means.
(b) S_xx , S_xy S_yy.
(c) Calculate the least squares estimates $\beta$ ₁ and $\beta$ ₀.
(d) Estimate the error variance.
(e) Determine the proportion of variation in y explained by x.

Question 27

Consider the data

(a) Calculate the least squares estimates $\beta$ ₁ and $\beta$ ₀.
(b) Estimate the error variance.
(c) Obtain a 95 % confidence interval for $\beta$ ₁. Can you conclude that the slope is different from 0?
(d) Determine the proportion of variation in y explained by x.

Question 28

Consider the data
(a) Calculate the least squares estimates $\beta$ ₁ and $\beta$ ₀.

(b) Estimate the error variance.
(c) Obtain a 95 % confidence interval for $\beta$ ₁. Can you conclude that the slope is different from 0?
(d) Find a 95% confidence interval for the mean response when
x = 8.

Question 29

An internet site lists the prices, y, of a used popular midsized model foreign car. The age, x, in years and the price(thousands $) are given in the table for a sample of six cars.

(a) Determine the least squares regression line.
(b) Estimate the price of a used car of this model whose age is 9.
(c) Give a 95% prediction interval for the price of a used car of age 9.
(d) Besides the uncertainty accounted for in the calculation in Part c, what else could lead to a serious mistake in the pre- diction.