Question 1

The regression line  has been fitted to the data points (4,11),(2,7),and (1,5).The sum of squares for error will be 10.0.

Accepted Answer

True

Question 2

The first-order linear model is sometimes called the simple linear regression model.

Accepted Answer

The first-order linear model is also known as the simple linear regression model. It involves fitting a straight line to the data points to establish a relationship between the independent and dependent variables. Therefore, option A is correct.

Question 3

The regression line  has been fitted to the data points (4,8),(2,5),and (1,2).The sum of the squared residuals will be:

Accepted Answer

D

Question 4

Another name for the residual term in a regression equation is random error.

Accepted Answer

The residual term in a regression equation represents the variation in the dependent variable that is not explained by the independent variable(s), which can be thought of as random error.

Question 5

Given the least squares regression line  :

Accepted Answer

The answer of Given the least squares regression line ...

Question 6

The vertical spread of the data points about the regression line is measured by the y-intercept.

Accepted Answer

The vertical spread of the data points about the regression line is measured by the residual standard error, which is not related to the y-intercept.

Question 7

Statisticians have shown that sample y-intercept b₀ and sample slope coefficient b₁ are unbiased estimators of the population regression parameters β₀ and β₁,respectively.

Accepted Answer

It is true that the sample y-intercept and sample slope coefficient are unbiased estimators of the population regression parameters.

Question 8

A regression analysis between sales (in $1000)and advertising (in $100)resulted in the following least squares line:  .This implies that if advertising is $600,then the predicted amount of sales (in dollars)is $125,000.

Accepted Answer

The least squares line is used to predict the value of the dependent variable (sales) based on the independent variable (advertising). The given line implies that for every increase of $100 in advertising, the predicted sales increase by $11,000. Therefore, if advertising is $600 (in hundreds), the predicted sales would be $11,000 * 6 = $66,000 (in hundreds) or $66,000 * 100 = $6,600, which is not $125,000. Hence, the given statement is false.

Question 9

The residuals are observations of the error variable ε.Consequently,the minimized sum of squared deviations is called the sum of squares for error,denoted SSE.

Accepted Answer

This statement is true that residuals are observations of the error variable epsilon and the minimized sum of squared deviations is called the sum of squares for error, denoted SSE.

Question 10

A direct relationship between an independent variable x and a dependent variably y means that the variables x and y increase or decrease together.

Accepted Answer

A direct relationship, also known as a positive relationship, means that as the independent variable increases, the dependent variable also increases, or as the independent variable decreases, the dependent variable also decreases.

Question 11

A regression analysis between weight (y in pounds)and height (x in inches)resulted in the following least squares line:  .This implies that if the height is increased by 1 inch,the weight is expected to increase by an average of 6 pounds.

Accepted Answer

According to the given information, the slope of the least squares line is 6. This means that for every 1 inch increase in height, the expected increase in weight is 6 pounds. Therefore, the statement "if the height is increased by 1 inch, the weight is expected to increase by an average of 6 pounds" is true.

Question 12

A simple linear regression equation is given by  .The point estimate of y when x = 4 is 20.45.

Accepted Answer

The answer of A simple linear regression equation is given...

Question 13

A regression analysis between sales (in $)and advertising (in $)resulted in the following least squares line:  .This implies that an increase of $1 in advertising is associated with an increase of $60 in sales.

Accepted Answer

The answer of A regression analysis between sales (in $)and...

Question 14

A regression analysis between weight (y in pounds)and height (x in inches)resulted in the following least squares line:  .This implies that if the height is increased by 1 inch,the weight,on average,is expected to:

Accepted Answer

The answer of A regression analysis between weight (y in...

Question 15

The method of least squares requires that the sum of the squared deviations between actual y values in the scatter diagram and y values predicted by the regression line be minimized.

Accepted Answer

This is correct as the method of least squares is specifically designed to minimize the sum of squared deviations between actual values and predicted values.

Question 16

If cov(x,y)= 7.5075 and  ,then the sample slope coefficient is 2.145.

Accepted Answer

The sample slope coefficient is estimated as b = cov(x, y)/var(x). Substituting the given values, we get b = 7.5075/11ea78b9_2e3b_6ad0_8379_a7ab8bcd02b0_TB4388_11 = 2.145. Therefore, the statement is true.

Question 17

The residual r_i is defined as the difference between the actual value y_i and the estimated value .

Accepted Answer

This is true as the residual is defined as the difference between the actual value and estimated value.

Question 18

An inverse relationship between an independent variable x and a dependent variably y means that as x increases,y decreases,and vice versa.

Accepted Answer

This is the definition of an inverse relationship between two variables.

Question 19

To create a deterministic model,we start with a probabilistic model that approximates the relationship we want to model.

Accepted Answer

A deterministic model does not start with a probabilistic model; instead, it is built on precise equations and inputs that produce a specific output without incorporating randomness or probability.

Question 20

If an estimated regression line has a y-intercept of 10 and a slope of 4,then when x = 2 the actual value of y is:

Accepted Answer

The actual value of y for a given x in a regression analysis can differ from the value predicted by the regression line due to the presence of error or variability in the data. The regression line provides an estimate or prediction, not the actual value.

Quiz 16: Simple Linear Regression and Correlation

The regression line has been fitted to the data points (4,11),(2,7),and (1,5).The sum of squares for error will be 10.0.

The first-order linear model is sometimes called the simple linear regression model.

The regression line has been fitted to the data points (4,8) ,(2,5) ,and (1,2) .The sum of the squared residuals will be:

Another name for the residual term in a regression equation is random error.

Given the least squares regression line :

The vertical spread of the data points about the regression line is measured by the y-intercept.

Statisticians have shown that sample y-intercept b₀ and sample slope coefficient b₁ are unbiased estimators of the population regression parameters β₀ and β₁,respectively.

A regression analysis between sales (in $1000)and advertising (in $100)resulted in the following least squares line: .This implies that if advertising is $600,then the predicted amount of sales (in dollars)is $125,000.

The residuals are observations of the error variable ε.Consequently,the minimized sum of squared deviations is called the sum of squares for error,denoted SSE.

A direct relationship between an independent variable x and a dependent variably y means that the variables x and y increase or decrease together.

A regression analysis between weight (y in pounds)and height (x in inches)resulted in the following least squares line: .This implies that if the height is increased by 1 inch,the weight is expected to increase by an average of 6 pounds.

A simple linear regression equation is given by .The point estimate of y when x = 4 is 20.45.

A regression analysis between sales (in $)and advertising (in $)resulted in the following least squares line: .This implies that an increase of $1 in advertising is associated with an increase of $60 in sales.

A regression analysis between weight (y in pounds) and height (x in inches) resulted in the following least squares line: .This implies that if the height is increased by 1 inch,the weight,on average,is expected to:

The method of least squares requires that the sum of the squared deviations between actual y values in the scatter diagram and y values predicted by the regression line be minimized.

If cov(x,y)= 7.5075 and ,then the sample slope coefficient is 2.145.

The residual r_i is defined as the difference between the actual value y_i and the estimated value .

An inverse relationship between an independent variable x and a dependent variably y means that as x increases,y decreases,and vice versa.

To create a deterministic model,we start with a probabilistic model that approximates the relationship we want to model.

If an estimated regression line has a y-intercept of 10 and a slope of 4,then when x = 2 the actual value of y is:

Quiz 16: Simple Linear Regression and Correlation

The regression line has been fitted to the data points (4,11),(2,7),and (1,5).The sum of squares for error will be 10.0.

The first-order linear model is sometimes called the simple linear regression model.

The regression line has been fitted to the data points (4,8) ,(2,5) ,and (1,2) .The sum of the squared residuals will be:

Another name for the residual term in a regression equation is random error.

Given the least squares regression line :

The vertical spread of the data points about the regression line is measured by the y-intercept.

Statisticians have shown that sample y-intercept b0 and sample slope coefficient b1 are unbiased estimators of the population regression parameters β0 and β1,respectively.

A regression analysis between sales (in $1000)and advertising (in $100)resulted in the following least squares line: .This implies that if advertising is $600,then the predicted amount of sales (in dollars)is $125,000.

The residuals are observations of the error variable ε.Consequently,the minimized sum of squared deviations is called the sum of squares for error,denoted SSE.

A direct relationship between an independent variable x and a dependent variably y means that the variables x and y increase or decrease together.

A regression analysis between weight (y in pounds)and height (x in inches)resulted in the following least squares line: .This implies that if the height is increased by 1 inch,the weight is expected to increase by an average of 6 pounds.

A simple linear regression equation is given by .The point estimate of y when x = 4 is 20.45.

A regression analysis between sales (in $)and advertising (in $)resulted in the following least squares line: .This implies that an increase of $1 in advertising is associated with an increase of $60 in sales.

A regression analysis between weight (y in pounds) and height (x in inches) resulted in the following least squares line: .This implies that if the height is increased by 1 inch,the weight,on average,is expected to:

The method of least squares requires that the sum of the squared deviations between actual y values in the scatter diagram and y values predicted by the regression line be minimized.

If cov(x,y)= 7.5075 and ,then the sample slope coefficient is 2.145.

The residual ri is defined as the difference between the actual value yi and the estimated value .

An inverse relationship between an independent variable x and a dependent variably y means that as x increases,y decreases,and vice versa.

To create a deterministic model,we start with a probabilistic model that approximates the relationship we want to model.

If an estimated regression line has a y-intercept of 10 and a slope of 4,then when x = 2 the actual value of y is:

Statisticians have shown that sample y-intercept b₀ and sample slope coefficient b₁ are unbiased estimators of the population regression parameters β₀ and β₁,respectively.

The residual r_i is defined as the difference between the actual value y_i and the estimated value .