Exam 13: Simple Linear Regression Analysis

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 Calculate the coefficient of determination.

A significant positive correlation between X and Y implies that changes in X cause Y to change.

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

In simple regression analysis the quantity that gives the amount by which Y (dependent variable)changes for a unit change in X (independent variable)is called the

The correlation coefficient may assume any value between

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

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

The range for r² is between 0 and 1 and the range for r is between ________

In a simple linear regression model,the coefficient of determination not only indicates the strength of the relationship between independent and dependent variable,but also shows whether the relationship is positive or negative.

When using simple regression analysis,if there is a strong correlation between the independent and dependent variable,then we can conclude that an increase in the value of the independent variable causes an increase in the value of the dependent variable.

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 estimated y intercept and slope and write the equation of the least squares regression line.

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).Residuals are calculated for all of the randomly selected six months and ordered from smallest to largest. Determine the normal score for the third residual in the ordered array.

The simple coefficient of determination is the proportion of total variation explained by the regression line.

A simple linear regression model is an equation that describes the straight-line relationship between a dependent variable and an independent variable.

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 and the strength is measured in pounds per square inch,MSE = 0.5, = 30, = 104. Determine the 95% confidence interval for the average strength of a metal sheet when the average heating time is 2.5 minutes.

An experiment was performed on a certain metal to determine if the strength is a function of heating time.The sample size consists of ten metal sheets.The simple linear regression equation is = 1 + 1X.The time is in minutes and the strength is measured in pounds per square inch.One of the ten metal sheets was heated for 4 minutes and the resulting strength was 6 lbs.per square inch.Calculate the value of the residual for this observation.

The notation refers to the average value of the dependent variable Y.

The _____ of the simple linear regression model is the value of y when the mean value of x is zero.

For a given data set,specific value of X,and a confidence level,if all the other factors are constant,the confidence interval for the mean value of Y will _______ be wider than the corresponding prediction interval for the individual value of Y.

The point estimate of the variance in a regression model is