Exam 13: Simple Linear Regression Analysis

Consider the following partial computer output from a simple linear regression analysis. S = 0.4862 R-Sq = ______ Analysis of Variance What is the predicted value of y when x = 9.00?

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. = 24 = 124 = 42 = 338 = 196 Determine the value of the F statistic.

The strength of the relationship between two quantitative variables can be measured by:

When there is positive autocorrelation,over time,negative error terms are followed by positive error terms and positive error terms are followed by negative error terms.

For the same value X (independent variable),the confidence interval for the average value of Y (dependent variable)is __________________ the prediction interval for the individual value of Y.

A data set with 7 observations yielded the following.Use the simple linear regression model. = 21.57 = 68.31 = 188.9 = 5,140.23 = 590.83 SSE = 1.06 Calculate the correlation coefficient.

Consider the following partial computer output from a simple linear regression analysis. S = 0.4862 R-Sq = ______ Analysis of Variance What is the coefficient of determination?

In simple linear regression analysis,we assume that the variance of the independent variable (X)is equal to the variance of the dependent variable (Y).

When the constant variance assumption holds,a plot of the residual versus x:

Consider the following partial computer output from a simple linear regression analysis. What is the estimated slope?

Consider the following partial computer output from a simple linear regression analysis. S = 0.4862 R-Sq = ______ Analysis of Variance Calculate the SSE

An experiment was performed on a certain metal to determine if the strength is a function of heating time.The simple linear regression equation is = 1 + 1X.The time is in minutes and the strength is measured in pounds per square inch. The 95% confidence interval for the slope is from .564 to 1.436.Can we reject $\beta$ ₁ = 0?

Use the following results obtained from a simple linear regression analysis with 12 observations. = 37.2895 - (1.2024)X r² = .6744 s_b = .2934 Test to determine if there is a significant negative relationship between the independent and dependent variable at $\alpha$ = .05.Give the test statistic and the resulting conclusion.

Consider the following partial computer output from a simple linear regression analysis. S = 0.4862 R-Sq = ______ Analysis of Variance Test H₀: ₁ = 0 versus Ha: ₁ $\neq$ 0 by setting = .001.What do you conclude about the relationship between y and x?

Regression Analysis The local grocery store wants to predict the daily sales in dollars.The manager believes that the amount of newspaper advertising significantly affects the store 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/Mega-Stat output given above summarizes the results of the regression model. What are the limits of the 95% confidence interval for the population slope?

The following results were obtained from a simple regression analysis: = 37.2895 - (1.2024)X r²= .6744 s_b = .2934 When X (independent variable)is equal to zero,the estimated value of Y (dependent variable)is equal to:

An experiment was performed on a certain metal to determine if the strength is a function of heating time.Results based on 10 metal sheets are given below.Use the simple linear regression model. = 30 = 104 = 40 = 178 = 134 Find the t statistic and test H₀: B₁ $\le$ 0 vs.H_a: B₁ > 0 at $\alpha$ = .05.

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

If r = -1,then we can conclude that there is a perfect relationship between X and Y.

A data set with 7 observations yielded the following.Use the simple linear regression model. = 21.57 = 68.31 = 188.9 = 5,140.23 = 590.83 SSE = 1.06 Find the rejection point for the t statistic ( = .05).Test H₀: $\beta$ ₁ $\le$ 0 vs.H_a: $\beta$ ₁ > 0.