Exam 13: Chi-Square Tests

A local tire dealer wants to predict the number of tires sold each month.He believes that the number of tires sold is a linear function of the amount of money invested in advertising.He randomly selects 6 months of data consisting of tire sales (in thousands of tires)and advertising expenditures (in thousands of dollars).Based on the data set with 6 observations,the simple linear regression equation of the least squares line is ŷ = 3 + 1x. MSE = 4 Use the least squares regression equation and estimate the monthly tire sales when advertising expenditures = $4,000.

A local tire dealer wants to predict the number of tires sold each month.He believes that the number of tires sold is a linear function of the amount of money invested in advertising.He randomly selects 6 months of data consisting of monthly tire sales (in thousands of tires)and monthly advertising expenditures (in thousands of dollars).The simple linear regression equation is ŷ = 3 + 1x.The dealer randomly selects one of the six observations,with a monthly sales value of 8,000 tires and monthly advertising expenditures of $7,000.Calculate the value of the residual for this observation.

In simple regression analysis,the standard error is ___________ greater than the standard deviation of y values.

In simple regression analysis,the quantity is called the __________ sum of squares.

An experiment was performed on a certain metal to determine if the strength is a function of heating time.Partial results based on a sample of 10 metal sheets are given below.The simple linear regression equation is = 1 + 1X.The time is in minutes,the strength is measured in pounds per square inch,MSE = 0.5, = 30,and = 104.Determine the 95 percent confidence interval for the average strength of a metal sheet when the average heating time is 2.5 minutes.

The ____________________ is the proportion of the total variation in the dependent variable explained by the regression model.

Consider the following partial computer output from a simple linear regression analysis. Calculate the correlation coefficient.

A data set with 7 observations yielded the following.Use the simple linear regression model. Calculate the coefficient of determination.

Which of the following is a violation of the independence assumption?

In simple regression analysis,if the correlation coefficient is a positive value,then

A local tire dealer wants to predict the number of tires sold each month.He believes that the number of tires sold is a linear function of the amount of money invested in advertising.He randomly selects 6 months of data consisting of tire sales (in thousands of tires)and advertising expenditures (in thousands of dollars).Based on the data set with 6 observations,the simple linear regression equation of the least squares line is ŷ = 3 + 1x. Using the sums of the squares given above,determine the 95 percent confidence interval for the slope.

The following results were obtained as part of a simple regression analysis.r² = .9162 F statistic from the F table = 3.59 Calculated value of F from the ANOVA table = 81.87 Α = .05 P-value = .000 The null hypothesis of no linear relationship between the dependent variable and the independent variable

The ____________ assumption requires that all variation around the regression line should be equal at all possible values (levels)of the ___________variable.

Regression Analysis A local grocery store wants to predict its daily sales in dollars.The manager believes that the amount of newspaper advertising significantly affects sales.He randomly selects 7 days of data consisting of daily grocery store sales (in thousands of dollars)and advertising expenditures (in thousands of dollars).The Excel/MegaStat output given above summarizes the results of the regression model.What are the limits of the 95 percent confidence interval for the population slope?

When the assumption of __________ residuals (error terms)is violated,the Durbin-Watson statistic is used to test to determine if there is significant _____________ among the residuals.

The estimated simple linear regression equation minimizes the sum of the squared deviations between each value of Y and the line.

The simple linear regression (least squares method)minimizes

When using simple linear regression,we would like to use confidence intervals for the ___________ and prediction intervals for the ___________ at a given value of x.

A local tire dealer wants to predict the number of tires sold each month.He believes that the number of tires sold is a linear function of the amount of money invested in advertising.He randomly selects 6 months of data consisting of tire sales (in thousands of tires)and advertising expenditures (in thousands of dollars).Based on the data set with 6 observations,the simple linear regression model yielded the following results. Calculate the standard error.

The ___________ the r² and the __________ the s (standard error),the stronger the relationship between the dependent variable and the independent variable.