Exploring Data: Bivariate Data
b
The formula shown above can be used to calculation: a) Relation Between Slope of Line (S) and Correlation Coefficient (b₁) b) Relation Between Slope of Line (b₁) and Correlation Coefficient (r) c) Relation Between X intercept (Sx) and Y intercept (Sy)
b
The goal of linear regression is to; a) Find the line of best fit b) Reduce ε to make the model predict the observed values as closely as possible c) Find the correlation coefficient
b
The line of best fit will ALWAYS pass through: a) the origin; (0,0) b) the centroid (average of x values, average of y) c) y-axis (1,0) d) x-axis (0,1)
d
The following predict equation,y= a logbx, is an example of a possible variable relationship. What format is the equation in? a) Linear b) Quadratic c) Exponential d) Logarithmic
a
The following scatter plot is an example of: a) Perfect Positive Correlation b) Perfect Negative Correlation c) Horizontal - No Correlation d) Vertical - No Correlation
b
The following scatter plot is an example of: a) Perfect Positive Correlation b) Perfect Negative Correlation c) Horizontal - No Correlation d) Vertical - No Correlation
c
The following scatter plot is an example of: a) Perfect Positive Correlation b) Perfect Negative Correlation c) Horizontal - No Correlation d) Vertical - No Correlation
d
The following scatter plot is an example of: a) Perfect Positive Correlation b) Perfect Negative Correlation c) Horizontal - No Correlation d) Vertical - No Correlation
a
The following scatterplot is an example of: a) No Correlation b) Positive Correlation c) High Positive Correlation d) Negative Correlation e) High Negative Correlation
b
The following scatterplot is an example of: a) No Correlation b) Positive Correlation c) High Positive Correlation d) Negative Correlation e) High Negative Correlation
c
The following scatterplot is an example of: a) No Correlation b) Positive Correlation c) High Positive Correlation d) Negative Correlation e) High Negative Correlation
d
The following scatterplot is an example of: a) No Correlation b) Positive Correlation c) High Positive Correlation d) Negative Correlation e) High Negative Correlation
e
The following scatterplot is an example of: a) No Correlation b) Positive Correlation c) High Positive Correlation d) Negative Correlation e) High Negative Correlation
a
The formula (Z=In(Y)) is used to describe a: a) Logarithmic Transformation b) Square Root Transformation c) Reciprocal Transformation d) Square Transformation e) Power Transformation
a
The formula above defines: a) The predicted value of Y for a given value of X b) The predicted value of X for a given value of Y c) The Y-intercept d) The Y centroid
c
The formula above defines: a) X intercept b) X axis centroid c) Average of all X Values d) Value of X
c
The formula above defines: a) Y intercept b) Y axis centroid c) Average of all Y Values d) Value of Y
Linear
A _____ relation is one that can be described using a straight line.
d
A correlation coefficient close to +1 indicates: a) Perfect Positive Correlation b) Perfect Negative Correlation c) No Correlation d) Strong Positive Correlation e) Strong Negative Correlation
e
A correlation coefficient close to -1 indicates: a) Perfect Positive Correlation b) Perfect Negative Correlation c) No Correlation d) Strong Positive Correlation e) Strong Negative Correlation d) Weak Correlation
d
A correlation coefficient close to 0 indicates: a) Perfect Positive Correlation b) Perfect Negative Correlation c) No Correlation d) Strong Positive Correlation e) Strong Negative Correlation d) Weak Correlation
a
A correlation coefficient of +1 indicates: a) Perfect Positive Correlation b) Perfect Negative Correlation c) No Correlation
b
A correlation coefficient of -1 indicates: a) Perfect Positive Correlation b) Perfect Negative Correlation c) No Correlation
c
A correlation coefficient of 0 indicates: a) Perfect Positive Correlation b) Perfect Negative Correlation c) No Correlation
Correlation Coefficent
A measure of the linear correlation between two variables X and Y, giving a value between +1 and −1.
Scatterplot
A plot of all ordered pairs of bivariate data on a coordinate axis system.
Residual Plot
A plot of residuals versus the predicted values of Y; used to assess the fit of a model.
a
A random sample of 10 office assistants hired within the last six months was selected from a large company. Each assistants experience (in months) at the time of hire and annual salary (in thousands of dollars) were recorded. If the observed paycheck of an assistant is $34,000, but the predicted paycheck was $33,512, this means... a) The office assistant received $488 more than the expected starting salary. b) The office assistant received $488 less than the expected starting salary c) The correlation is weak
a
A random sample of 10 office assistants hired within the last six months was selected from a large company. Each assistants experience (in months) at the time of hire and annual salary (in thousands of dollars) were recorded. If the equation for the line of best fit is: y=20.432 + 1.09x What would inputing 6 in for x calculate? a) Starting salary for 6 months experience b) Months experience for salary of 1.09 × 6 c) Average salary for 6 months of experience d) Average experience for a salary of 1.09 × 6
b
A random sample of 10 office assistants hired within the last six months was selected from a large company. Each assistants experience (in months) at the time of hire and annual salary (in thousands of dollars) were recorded. The coefficient of determination is 90.52%, this can be interpreted as: a) 9.5% of the variation among starting salaries is attributable to prior experience; 90.52% of variation among salaries is due to some other factor b) 90.52% of the variation among starting salaries is attributable to prior experience; 9.5% of variation among salaries is due to some other factor c) The correlation between starting salary for office assistants and their prior experience is high d) The correlation between prior experience and starting salary for office assistants is high
a
A random sample of 10 office assistants hired within the last six months was selected from a large company. Each assistants experience (in months) at the time of hire and annual salary (in thousands of dollars) were recorded. y=20.432 + 1.09x The slope of the line can be interpreted as meaning: a) For every month's additional experience at the time of hiring, the starting salary increases by an average of $1,090. b) For every month's additional experience at the time of hiring, the starting salary increases by an average of $20,432. c) The predicted salary of an inexperienced office assistant (0 months) is $1,090 d) The predicted salary of an inexperienced office assistant (0 months) is $20,432
d
A random sample of 10 office assistants hired within the last six months was selected from a large company. Each assistants experience (in months) at the time of hire and annual salary (in thousands of dollars) were recorded. y=20.432 + 1.09x The y-intercept can be interpreted as meaning: a) For every month's additional experience at the time of hiring, the starting salary increases by an average of $1,090. b) For every month's additional experience at the time of hiring, the starting salary increases by an average of $20,432. c) The predicted salary of an inexperienced office assistant (0 months) is $1,090 d) The predicted salary of an inexperienced office assistant (0 months) is $20,432
Logarithmic
A type of transformation used to linearize the regression model when the relationship between Y and X suggest a model with a constantly increasing slope.
Outlier
An observation that is uncharacteristically different from the rest of the data.
b
An observation that is uncharacteristically different from the rest of the data. a) Influential Observation b) Outlier
Influential Observation
An observation that strongly affects a statistic.
a
An observation that strongly affects a statistic. a) Influential Observation b) Outlier
c
As x increases there is an decreases in the shift of values of y. The correlation can be defined as: a) No correlation b) Positive Correlation c) Negative Correlation
b
As x increases there is an increase in the shift of values of y. The correlation can be defined as: a) No correlation b) Positive Correlation c) Negative Correlation
a
As x increases there is no definite shift in the values of y. The correlation can be defined as: a) No correlation b) Positive Correlation c) Negative Correlation
a
It can be shown that for linear regression, R² (coefficient of determination) is equal to: a) Coefficient of Linear Correlation² (squared) b) Line of Best Fit c) Coefficient of Linear Correlation d) Y-intercept e) X-intercept
Coefficient of Determination
Measures the percent of variation in Y-values attributable to the variation in X-values.
b
Bivariate data with a combination of what type of variables is commonly arranged using a back-to-back or side-by-side display? a) Both Qualitative b) Qualitative; quantitative c) Both Quantitative
a
Bivariate data with a combination of what type of variables is commonly arranged using a contingency table or cross-tabulation? a) Both Qualitative b) Qualitative; quantitative c) Both Quantitative
d
Calculating what value find the equation of the line that best describes the relationship between two variables? a) Coefficent of Determination b) Coefficient of Linear Correlation c) Correlation Analysis d) Regression Analysis
b
Calculating what value measures how well a straight line describes the scattered diagram of ordered pairs? a) Coefficent of Determination b) Coefficient of Linear Correlation c) Correlation Analysis d) Regression Analysis
a
Measures the percent of variation in Y-values attributable to the variation in X-values; explained by the linear relation by X- and Y- values. a) Coefficient of Determination b) Coefficient of Linear Correlation
a
The following predict equation, y=b₀+b₁x, is an example of a possible variable relationship. What format is the equation in? a) Linear b) Quadratic c) Exponential d) Logarithmic
Bivariate Data
Data that consists of two values of different variables obtained from the same population element.
Negative Correlation
Defined as an decrease in the shift of values of y as x increases.
Positive Correlation
Defined as an increase in the shift of values of y as x increases.
No Correlation
Defined as no definite shift in the values of y when x increases.
a
Denoted by 'r'. a) Coefficient of Determination b) Coefficient of Linear Correlation
b
Denoted by 'r²'. a) Coefficient of Determination b) Coefficient of Linear Correlation
Shows
If a residual plot shows/does not show any patterns or trends, it is an indication that the linear model is not appropriate.
c
If data forms a straight horizontal or vertical line, there is: a) Perfect Correlation b) Perfect Negative Correlation c) No Correlation d) Perfect Positive Correlation
b
If there is considerable difference between the correlation coefficients computed with and without a specific observation, the observation can be considered to be [a]: a) Outlier b) Influential Observation
b
If there is considerable difference between the linear regression (line of best fit) computed with and without a specific observation, the observation can be considered to be [a]: a) Outlier b) Influential Observation
b
In a set of ordered pairs (x,y), the variable x is the: a) dependent variable b) independent variable
a
In a set of ordered pairs (x,y), the variable y is the: a) dependent variable b) independent variable
y
In a set of ordered pairs (x,y), which variable is the dependent variable?
x
In a set of ordered pairs (x,y), which variable is the independent variable?
a
In the formula above, the symbol β₀ represents: a) the estimated y-intercept of the regression line b) the estimated slope of the regression line c) the difference between the observed value of Y and the predicted value of Y
b
In the formula above, the symbol β₁ represents: a) the estimated y-intercept of the regression line b) the estimated slope of the regression line c) the difference between the observed value of Y and the predicted value of
c
In the formula above, the symbol ε represents: a) the estimated y-intercept of the regression line b) the estimated slope of the regression line c) the difference between the observed value of Y and the predicted value of
Perfect Correlation
Occurs when all data points fall exactly along a straight line.
a
Occurs when all data points fall exactly along a straight line. a) Perfect Correlation b) Perfect Negative Correlation c) No Correlation d) Perfect Positive Correlation
Coefficient of Determination
Percent of variation in the response variable explained by its linear relationship with the explanatory variable.
Linear Correlation
Refers to the straight-line relationships between two variables.
Coefficient Correlation
Reflects the consistency of the effect that a change in one variable has on the other.
ε
Represents error or residual; the difference between the observed and predicted value.
a
Slope (b₁) represents: a) Predicted change in y per unit increase in x b) Predicted change in y per unit decrease in x c) Where the line best fit intersects the y axis
b
The following predict equation, y = a+bx+c², is an example of a possible variable relationship. What format is the equation in? a) Linear b) Quadratic c) Exponential d) Logarithmic
c
The following predict equation, y=a(b^x), is an example of a possible variable relationship. What format is the equation in? a) Linear b) Quadratic c) Exponential d) Logarithmic
d
The linear relation between two variable is given by the following equation for the linear regression line: Y=β₀+β₁X+e What does 'B₁' represent? a) Independent Variable b) Dependent Variable c) Y-Intercept d) Slope of the Line e) Account for Random Error
b
The linear relation between two variable is given by the following equation for the linear regression line: Y=β₀+β₁X+e What does 'X' represent? a) Independent Variable b) Dependent Variable c) Y-Intercept d) Slope of the Line e) Account for Random Error
b
The linear relation between two variable is given by the following equation for the linear regression line: Y=β₀+β₁X+e What does 'Y' represent? a) Independent Variable b) Dependent Variable c) Y-Intercept d) Slope of the Line e) Account for Random Error
c
The linear relation between two variable is given by the following equation for the linear regression line: Y=β₀+β₁X+ε What does 'B₀' represent? a) Independent Variable b) Dependent Variable c) Y-Intercept d) Slope of the Line e) Account for Random Error
e
The linear relation between two variable is given by the following equation for the linear regression line: Y=β₀+β₁X+ε What does 'ε' represent? a) Independent Variable b) Dependent Variable c) Y-Intercept d) Slope of the Line e) Account for Random Error
Coefficient Correlation
The numerical measure of the strength of the linear relationship between two variables; represented by r.
b
The numerical measure of the strength of the linear relationship between two variables; represented by r. a) Coefficient of Determination b) Coefficient of Linear Correlation
Linear Correlation
The preciseness of the shift in y as x increases determines the strength of...
a
The relationship of the scatterplot above can be best described as a: a) Linear Regression with a Positive Slope b) Linear Regression with a Negative Slope c) Curvilinear Regression (Quadratic) d) No Relationship
b
The relationship of the scatterplot above can be best described as a: a) Linear Regression with a Positive Slope b) Linear Regression with a Negative Slope c) Curvilinear Regression (Quadratic) d) No Relationship
c
The relationship of the scatterplot above can be best described as a: a) Linear Regression with a Positive Slope b) Linear Regression with a Negative Slope c) Curvilinear Regression (Quadratic) d) No Relationship
d
The relationship of the scatterplot above can be best described as a: a) Linear Regression with a Positive Slope b) Linear Regression with a Negative Slope c) Curvilinear Regression (Quadratic) d) No Relationship
Correlation
The strength of a linear relationship between two variables.
c
The y-intercept (y) represents: a) Predicted change in y per unit increase in x b) Predicted change in y per unit decrease in x c) Where the line best fit intersects the y axis
True
True or False? One variable obtained from a population in a bivariate data set can be qualitative, while the other can be quantitative.
Scatterplot
Used to describe the nature, degree, and direction of the relation between two variables x and y, where (x,y) gives pair of measurements.
a
Used to linearize the regression model when the relationship between Y and X suggest a model with a constantly increasing slope. a) Logarithmic Transformation b) Square Root Transformation c) Reciprocal Transformation d) Square Transformation e) Power Transformation
Separate
When bivariate data results from on qualitative, one quantitative variable, the quantitative values are viewed as the same/separate samples.
f
When bivariate data results from one qualitative and one quantitative variable, the data is often arranged using a: a) Bar Graph b) Pie Chart c) Contingency Table d) Stemplot e) Cross Tabulation f) Back-to-Back or Side-by-Side Display
f
When bivariate data results from two qualitative variables, the data is often arranged using a: a) Bar Graph b) Pie Chart c) Contingency Table d) Stemplot e) Cross Tabulation f) C and E g) A and B
b
When bivariate data results from two quantitive variable, the data is often arranges as (a): a) Bar Graph b) Scatterplot c) Contingency Table d) Stemplot e) Cross Tabulation f) Back-to-Back or Side-by-Side Display
c
Which of the following predict equations, or models is in exponential format? a) y=b₀+b₁x b) y = a+bx+c² c) y=a(b^x) d) y= a logbx
a
Which of the following predict equations, or models is in linear format? a) y=b₀+b₁x b) y = a+bx+c² c) y=a(b^x) d) y= a logbx
d
Which of the following predict equations, or models is in logarithmic format? a) y=b₀+b₁x b) y = a+bx+c² c) y=a(b^x) d) y= a logbx
b
Which of the following predict equations, or models is in quadratic format? a) y=b₀+b₁x b) y = a+bx+c² c) y=a(b^x) d) y= a logbx
