HW9
What distribution is used to test the significance of the population coefficient of determination? F-distribution Student's t distribution with df = n - 2 Student's t distribution with df = n - 1 standard normal distribution
F-distribution
In a regression analysis if R2 = 1, then SSE must be equal to zero SSE can be any positive value SSE must be negative SSE must also be equal to one
SSE must be equal to zero
In a regression analysis if R2 = 0, then SSR = 0 SSR = SST SSE = 1 SSR = SSE
SSR = 0
What would you conclude in the test of the significance of the slope if you used α = 0.01 instead? We would fail to reject the null hypothesis that the population slope is equal to 0, and conclude that there is no relationship between the hours of sleep and the age of the adult. We would reject the null hypothesis that the population slope is equal to 0, and conclude that there is a relationship between the hours of sleep and the age of the adult. We would fail to reject the null hypothesis that the population slope is equal to 0, and conclude that there is a relationship between the hours of sleep and the age of the adult. We would fail to reject the null hypothesis, and conclude that there is no negative relationship between the hours of sleep and the age of the adult.
We would fail to reject the null hypothesis that the population slope is equal to 0, and conclude that there is no relationship between the hours of sleep and the age of the adult.
Regression analysis was applied to analyze the relationship between demand for a product (y) and the price of the product (x), and the following estimated regression equation was obtained:y^=120−10xBased on the above estimated regression equation, if the price is increased by 5 units, then the demand is expected to, on average, decrease by 50 units increase by 50 units increase by 70 units increase by 120 units
decrease by 50 units
The model developed from sample data that has the form y^=b0+b1x is known as the estimated regression equation regression equation regression model correlation equation
estimated regression equation
A regression analysis between sales (y in $1000) and advertising (xin dollars) resulted in the following equation y^=100,000+0.5x The above equation implies that an increase of $1 in advertising is associated with an average increase of $500 in sales increase of $1 in advertising is associated with an average increase of $100,500 in sales increase of $1 in advertising is associated with an average increase of $0.5 in sales increase of $0.5 in advertising is associated with an average increase of $500 in sales
increase of $1 in advertising is associated with an average increase of $500 in sales
In the regression analysis, the variable that is being explained is called the dependent variable is called the independent variable is called the intervening variable is usually denoted by x
is called the dependent variable
Larger value of R2 is desirable because it implies that the estimated regression equation fits the data well. is undesirable because it implies that a large percentage of variation in the dependent variable remains unexplained. is not important. Generally, one should not pay attention to the values of R2 which should only be analyzed only in specific applications. is desirable sometimes and is not desirable other times. It depends on the analyzed problem.
is desirable because it implies that the estimated regression equation fits the data well.
If the coefficient of correlation is a negative value, then the regression equation must have a positive slope must have a negative slope could have either a positive or a negative slope must have a positive y-intercept
must have a negative slope
Regression analysis is a statistical procedure for developing a mathematical equation that describes how one dependent and one or more independent variables are related several independent and several dependent variables are related one independent and one or more dependent variables are related None of the suggested alternatives is correct
one dependent and one or more independent variables are related
Which technique enables us to describe a straight line that best fits observations characterized by a pair of values (x, y)? simple regression analysis correlation analysis analysis of variance hypothesis testing
simple regression analysis
Which of the following measures how consistent the slope of the regression equation would be if several sets of samples from the population were selected and the regression equations were derived for each of them? standard error of the slope standard error of the estimate coefficient of determination correlation coefficient
standard error of the slope
If the coefficient of determination is equal to 0.8, then the percentage of variation in the dependent variable explained by the variation in the independent variable is 80% the percentage of variation in the dependent variable explained by the variation in the independent variable is 0.8% the percentage of variation in the independent variable explained by the variation in the dependent variable is 80% the percentage of variation in the independent variable explained by the variation in the dependent variable is 0.8%
the percentage of variation in the dependent variable explained by the variation in the independent variable is 80%
The equation that describes how the dependent variable (y) is related to the independent variable (x) in the population is called the regression model the correlation model the regression equation the estimated regression equation
the regression model
The correlation coefficient is useful and helps determine the strength and the direction of the relationship between the dependent and the independent variables the equation that described the relationship between two variables a specific value of the dependent variable for a given value of the independent variable None of the suggested alternatives is correct
the strength and the direction of the relationship between the dependent and the independent variables
When describing the equation that best fits the observations characterized by (x, y), the least squares method minimizes the sum of squares error the sum of deviations of actual values y from the predicted values y^ the sum of absolute values of deviations of actual values y from the predicted values y^ the total sum of squares
the sum of squares error
Which of the following measures the variation in the dependent variable explained by variables other than the independent variable in the simple regression analysis? the sum of squares error the sum of squares regression the total sum of squares the standard error
the sum of squares error
In the estimated regression equation y^=b0+b1x the value of b0represents the y-intercept of the straight line the slope of the straight line the predicted value of y for a given a an independent variable
the y-intercept of the straight line
Which of the following measures the total variation in the dependent variable in simple regression analysis? total sum of squares sum of squares regression sum of squares error standard error
total sum of squares
In a regression analysis if SSE = 100 and SSR = 700, then the coefficient of determination is equal to 0.875 0.125 7 0.1429
.875
efer to the Exhibit Cape May Realty. Testing the significance of the slope coefficient at α = 0.10, one can conclude that Because the p-value < 0.10, we can reject the null hypothesis. Therefore, there is enough evidence to say that the population slope coefficient is different from zero. Because the p-value < 0.10, we can reject the null hypothesis. Therefore, there is enough evidence to say that the population slope coefficient is greater than zero. Because the p-value < 0.10, we can reject the null hypothesis. Therefore, there is enough evidence to say that the square footage has no effect on the property rental rate. Because the p-value < 0.10, we fail to reject the null hypothesis Therefore, there is enough evidence to say that there is no relationship between square footage and property rental rate.
Because the p-value < 0.10, we can reject the null hypothesis. Therefore, there is enough evidence to say that the population slope coefficient is different from zero.
Think about testing the significance of the slope of the regression equation. Which one of the following statements is correct using α= 0.10? Because the p-value for the slope is 0.015, we can reject the null hypothesis and conclude that there is a relationship between the hours of sleep and the age of the adult. Because the p-value for the slope is 0.015, we fail to reject the null hypothesis and conclude that there is a relationship between the hours of sleep and the age of the adult. Because the p-value for the slope is 0.015, we can reject the null hypothesis and conclude that there is no relationship between the hours of sleep and the age of the adult. Because the p-value for the slope is 0.015, we fail to reject the null hypothesis and conclude that there is no relationship between the hours of sleep and the age of the adult.
Because the p-value for the slope is 0.015, we can reject the null hypothesis and conclude that there is a relationship between the hours of sleep and the age of the adult.
