## Essentials of Statistics Study Set 1

Statistics

## Quiz 12 :

Simple Linear Regression

Looking for Business Statistics & Analytics Homework Help?

Q33 Q33 Q33

Regression analysis was applied between demand for a product Y) and the price of the product X), and the following estimated regression equation was obtained. = 120 - 10 X
Based on the above estimated regression equation, if price is increased by 2 units, then demand is expected to

Free

Unlocked

Multiple Choice

Q52 Q52 Q52

Regression analysis was applied between sales in $1000) and advertising in $100) and the following regression function was obtained. = 500 + 4 X
Based on the above estimated regression line if advertising is $10,000, then the point estimate for sales in dollars) is

Free

Unlocked

Multiple Choice

Q60 Q60 Q60

Regression analysis was applied between sales in $10,000) and advertising in $100) and the following regression function was obtained. = 50 + 8 X
Based on the above estimated regression line if advertising is $1,000, then the point estimate for sales in dollars) is

Free

Unlocked

Multiple Choice

Q63 Q63 Q63

Regression analysis was applied between sales Y in $1,000) and advertising X in $100), and the following estimated regression equation was obtained. = 80 + 6.2 X
Based on the above estimated regression line, if advertising is $10,000, then the point estimate for sales in dollars) is

Free

Unlocked

Multiple Choice

Q78 Q78 Q78

Exhibit 12-4
Regression analysis was applied between sales data Y in $1,000s) and advertising data x in $100s) and the following information was obtained.
= 12 + 1.8 x
n = 17
SSR = 225
SSE = 75
Sb₁ = 0.2683
-Refer to Exhibit 12-4. Based on the above estimated regression equation, if advertising is $3,000, then the point estimate for sales in dollars) is

Free

Unlocked

Multiple Choice

Q79 Q79 Q79

Exhibit 12-4
Regression analysis was applied between sales data Y in $1,000s) and advertising data x in $100s) and the following information was obtained.
= 12 + 1.8 x
n = 17
SSR = 225
SSE = 75
Sb₁ = 0.2683
-Refer to Exhibit 12-4. The F statistic computed from the above data is

Free

Unlocked

Multiple Choice

Q80 Q80 Q80

Exhibit 12-4
Regression analysis was applied between sales data Y in $1,000s) and advertising data x in $100s) and the following information was obtained.
= 12 + 1.8 x
n = 17
SSR = 225
SSE = 75
Sb₁ = 0.2683
-Refer to Exhibit 12-4. To perform an F test, the p-value is

Free

Unlocked

Multiple Choice

Q81 Q81 Q81

Exhibit 12-4
Regression analysis was applied between sales data Y in $1,000s) and advertising data x in $100s) and the following information was obtained.
= 12 + 1.8 x
n = 17
SSR = 225
SSE = 75
Sb₁ = 0.2683
-Refer to Exhibit 12-4. The t statistic for testing the significance of the slope is

Free

Unlocked

Multiple Choice

Q82 Q82 Q82

Exhibit 12-4
Regression analysis was applied between sales data Y in $1,000s) and advertising data x in $100s) and the following information was obtained.
= 12 + 1.8 x
n = 17
SSR = 225
SSE = 75
Sb₁ = 0.2683
-Refer to Exhibit 12-4. The critical t value for testing the significance of the slope at 95% confidence is

Free

Unlocked

Multiple Choice

Q114 Q114 Q114

Exhibit 12-10
The following information regarding a dependent variable Y and an independent variable X is provided.
-Assume you have noted the following prices for paperback books and the number of pages that each book contains.
a. Develop a least-squares estimated regression line.
b. Compute the coefficient of determination and explain its meaning.
c. Compute the correlation coefficient between the price and the number of pages. Test to see if x and y are related. Use α = 0.10.

Free

Unlocked

Essay

Q115 Q115 Q115

Exhibit 12-10
The following information regarding a dependent variable Y and an independent variable X is provided.
-Assume you have noted the following prices for books and the number of pages that each book contains.
a. Perform an F test and determine if the price and the number of pages of the books are related. Let α = 0.01.
b. Perform a t test and determine if the price and the number of pages of the books are related. Let α = 0.01.
c. Develop a 90% confidence interval for estimating the average price of books that contain 800 pages.
d. Develop a 90% confidence interval to estimate the price of a specific book that has 800 pages.

Free

Unlocked

Essay

Q116 Q116 Q116

Exhibit 12-10
The following information regarding a dependent variable Y and an independent variable X is provided.
-The following data represent the number of flash drives sold per day at a local computer shop and their prices.
a. Develop a least-squares regression line and explain what the slope of the line indicates.
b. Compute the coefficient of determination and comment on the strength of relationship between x and y.
c. Compute the sample correlation coefficient between the price and the number of flash drives sold. Use α= 0.01 to test the relationship between x and y.

Free

Unlocked

Essay

Q117 Q117 Q117

Exhibit 12-10
The following information regarding a dependent variable Y and an independent variable X is provided.
-The following data represent the number of flash drives sold per day at a local computer shop and their prices.
a. Perform an F test and determine if the price and the number of flash drives sold are related. Let
α = 0.01.
b. Perform a t test and determine if the price and the number of flash drives sold are related. Let
α = 0.01.

Free

Unlocked

Essay

Q118 Q118 Q118

Shown below is a portion of a computer output for a regression analysis relating Y demand) and X unit price).
a. Perform a t test and determine whether or not demand and unit price are related. Let α = 0.05.
b. Perform an F test and determine whether or not demand and unit price are related. Let α = 0.05.
c. Compute the coefficient of determination and fully interpret its meaning. Be very specific.
d. Compute the coefficient of correlation and explain the relationship between demand and unit price.

Free

Unlocked

Essay

Q119 Q119 Q119

Given below are four observations collected in a regression study on two variables x independent variable) and y dependent variable).
a. Develop the least squares estimated regression equation.
b. At 95% confidence, perform a t test and determine whether or not the slope is significantly different from zero.
c. Perform an F test to determine whether or not the model is significant. Let α = 0.05.
d. Compute the coefficient of determination.

Free

Unlocked

Essay

Q120 Q120 Q120

Below you are given a partial computer output based on a sample of 8 observations, relating an independent variable x) and a dependent variable y).
a. Develop the estimated regression line.
b. At α = 0.05, test for the significance of the slope.
c. At α = 0.05, perform an F test.
d. Determine the coefficient of determination.

Free

Unlocked

Essay

Q121 Q121 Q121

Below you are given a partial computer output based on a sample of 8 observations, relating an independent variable x) and a dependent variable y).
Analysis of Variance
SOURCE SS
Regression 400
Error Residual) 138
a. Develop the estimated regression line.
b. At α = 0.05, test for the significance of the slope.
c. At α = 0.05, perform an F test.
d. Determine the coefficient of determination.

Free

Unlocked

Essay

Q122 Q122 Q122

Given below are five observations collected in a regression study on two variables x independent variable) and y dependent variable).
a. Develop the least squares estimated regression equation
b. At 95% confidence, perform a t test and determine whether or not the slope is significantly different from zero.
c. Perform an F test to determine whether or not the model is significant. Let α = 0.05.
d. Compute the coefficient of determination.
e. Compute the coefficient of correlation.

Free

Unlocked

Essay

Q123 Q123 Q123

Below you are given a partial computer output based on a sample of 14 observations, relating an independent variable x) and a dependent variable y).
Analysis of Variance
SOURCE SS
Regression 958.584
Error Residual)
Total 1021.429
a. Develop the estimated regression line.
b. At α = 0.05, test for the significance of the slope.
c. At α = 0.05, perform an F test.
d. Determine the coefficient of determination.
e. Determine the coefficient of correlation.

Free

Unlocked

Essay

Q124 Q124 Q124

Below you are given a partial computer output based on a sample of 21 observations, relating an independent variable x) and a dependent variable y).
Analysis of Variance
SOURCE SS
Regression 1,759.481
Error 259.186
a. Develop the estimated regression line.
b. At α = 0.05, test for the significance of the slope.
c. At α = 0.05, perform an F test.
d. Determine the coefficient of determination.
e. Determine the coefficient of correlation.

Free

Unlocked

Essay

Q125 Q125 Q125

An automobile dealer wants to see if there is a relationship between monthly sales and the interest rate. A random sample of 4 months was taken. The results of the sample are presented below. The estimated least squares regression equation is
= 75.061 - 6.254X
Y X
Monthly Sales Interest Rate In Percent)
22 9.2
20 7.6
10 10.4
45 5.3
a. Obtain a measure of how well the estimated regression line fits the data.
b. You want to test to see if there is a significant relationship between the interest rate and monthly sales at the 1% level of significance. State the null and alternative hypotheses.
c. At 99% confidence, test the hypotheses.
d. Construct a 99% confidence interval for the average monthly sales for all months with a 10% interest rate.
e. Construct a 99% confidence interval for the monthly sales of one month with a 10% interest rate.

Free

Unlocked

Essay

Q126 Q126 Q126

Jason believes that the sales of coffee at his coffee shop depend upon the weather. He has taken a sample of 6 days. Below you are given the results of the sample.
a. Which variable is the dependent variable?
b. Compute the least squares estimated line.
c. Compute the correlation coefficient between temperature and the sales of coffee.
d. Is there a significant relationship between the sales of coffee and temperature? Use a .05 level of significance. Be sure to state the null and alternative hypotheses.
e. Predict sales of a 90 degree day.

Free

Unlocked

Essay

Q127 Q127 Q127

Researchers have collected data on the hours of television watched in a day and the age of a person. You are given the data below.
a. Determine which variable is the dependent variable.
b. Compute the least squares estimated line.
c. Is there a significant relationship between the two variables? Use a .05 level of significance. Be sure to state the null and alternative hypotheses.
d. Compute the coefficient of determination. How would you interpret this value?

Free

Unlocked

Essay

Q128 Q128 Q128

Given below are seven observations collected in a regression study on two variables, X independent variable) and Y dependent variable).
a. Develop the least squares estimated regression equation.
b. At 95% confidence, perform a t test and determine whether or not the slope is significantly different from zero.
c. Perform an F test to determine whether or not the model is significant. Let α = 0.05.
d. Compute the coefficient of determination.

Free

Unlocked

Essay

Q129 Q129 Q129

The owner of a retail store randomly selected the following weekly data on profits and advertising cost.
a. Write down the appropriate linear relationship between advertising cost and profits. Which is the dependent variable? Which is the independent variable?
b. Calculate the least squares estimated regression line.
c. Predict the profits for a week when $200 is spent on advertising.
d. At 95% confidence, test to determine if the relationship between advertising costs and profits is statistically significant.
e. Calculate the coefficient of determination.

Free

Unlocked

Essay

Q130 Q130 Q130

The owner of a bakery wants to analyze the relationship between the expenditure of a customer and the customer's income. A sample of 5 customers is taken and the following information was obtained.
The least squares estimated line is = 4.348 + 0.0826 X.
a. Obtain a measure of how well the estimated regression line fits the data.
b. You want to test to see if there is a significant relationship between expenditure and income at the 5% level of significance. Be sure to state the null and alternative hypotheses.
c. Construct a 95% confidence interval estimate for the average expenditure for all customers with an income of $20,000.
d. Construct a 95% confidence interval estimate for the expenditure of one customer whose income is $20,000.

Free

Unlocked

Essay

Q131 Q131 Q131

Below you are given information on annual income and years of college education.
a. Develop the least squares regression equation.
b. Estimate the yearly income of an individual with 6 years of college education.
c. Compute the coefficient of determination.
d. Use a t test to determine whether the slope is significantly different from zero. Let α = 0.05.
e. At 95% confidence, perform an F test and determine whether or not the model is significant.

Free

Unlocked

Essay

Q132 Q132 Q132

Below you are given information on a woman's age and her annual expenditure on purchase of books.
a. Develop the least squares regression equation.
b. Compute the coefficient of determination.
c. Use a t test to determine whether the slope is significantly different from zero. Let α = 0.05.
d. At 95% confidence, perform an F test and determine whether or not the model is significant.

Free

Unlocked

Essay

Q133 Q133 Q133

The following data shows the yearly income in $1,000) and age of a sample of seven individuals.
a. Develop the least squares regression equation.
b. Estimate the yearly income of a 30-year-old individual.
c. Compute the coefficient of determination.
d. Use a t test to determine whether the slope is significantly different from zero. Let α = 0.05.
e. At 95% confidence, perform an F test and determine whether or not the model is significant.

Free

Unlocked

Essay

Q134 Q134 Q134

The following data show the results of an aptitude test Y) and the grade point average of 10 students.
a. Develop a least squares estimated regression line.
b. Compute the coefficient of determination and comment on the strength of the regression relationship.
c. Is the slope significant? Use a t test and let α = 0.05.
d. At 95% confidence, test to determine if the model is significant i.e., perform an F test).

Free

Unlocked

Essay