OIS 3440 midterm 3

Given the data below, one ran the simple regression analysis of Y on X. The relationship between Y and X is

not significant at the alpha = 10 percent level.

A study was recently performed by the Internal Revenue Service to determine how much tip income waiters and waitresses should make based on the size of the bill at each table. A random sample of bills and resulting tips were collected. These data are shown as follows: Based upon these data, what is the approximate predicted value for tips if the total bill is $100?

$20.61

A study was done in which the high daily temperature and the number of traffic accidents within the city were recorded. These sample data are shown as follows: Given this data the sample correlation is:

.57

The following data for the dependent variable, y, and the independent variable, x, have been collected using simple random sampling Compute the correlation coefficient

.89

The following regression output is available. Notice that some of the values are missing. Given this information, what is the standard error of the estimate for the regression model?

About 1.98

A recent study by a major financial investment company was interested in determining whether the annual percentage change in stock price for companies is linearly related to the annual percent change in profits for the company. The following data was determined for 7 randomly selected companies: Based upon this sample information, what portion of variation in stock price percentage change is explained by the percent change in yearly profit?

About 49 percent

Consider the following partially completed computer printout for a regression analysis where the dependent variable is the price of a personal computer and the independent variable is the size of the hard drive. Based on the information provided, what is the F statistic?

About 69.5

In analyzing the relationship between two variables, a scatter plot can be used to detect which of the following?

All of the above

The following regression output is available. Notice that some of the values are missing. Given this information, what percent of the variation in the y variable is explained by the independent variable?

Approximately 57 percent

Consider the following partially completed computer printout for a regression analysis where the dependent variable is the price of a personal computer and the independent variable is the size of the hard drive.

Approximately 690.50

An industry study was recently conducted in which the sample correlation between units sold and marketing expenses was 0.57. The sample size for the study included 15 companies. Based on the sample results, test to determine whether there is a significant positive correlation between these two variables. Use an alpha = 0.05

Because t = 2.50 > 1.7709, reject the null hypothesis. There is sufficient evidence to conclude there is a positive linear relationship between sales units and marketing expense for companies in this industry.

Residual analysis is conducted to check whether regression assumptions are met. Which of the following is not an assumption made in simple linear regression?

Errors are linearly related to x.

A research study has stated that the taxes paid by individuals is correlated at a .78 value with the age of the individual. Given this, the scatter plot would show points that would fall on straight line on a slope equal to .78.

False

If two variables are highly correlated, it not only means that they are linearly related, it also means that a change in one variable will cause a change in the other variable.

False

In developing a scatter plot, the decision maker has the option of connecting the points or not

False

The sign on the intercept coefficient in a simple regression model will always be the same as the sign on the correlation coefficient.

False

A recent study of 15 shoppers showed that the correlation between the time spent in the store and the dollars spent was 0.235. Using a significance level equal to 0.05, which of the following is the appropriate null hypothesis to test whether the population correlation is zero?

H0 : ρ = 0.0

It is believed that number of people who attend a Mardi Gras parade each year depends on the temperature that day. A regression has been conducted on a sample of years where the temperature ranged from 28 to 64 degrees and the number of people attending ranged from 8400 to 14,600. The regression equation was found to be y^ = 2378 + 191x. Which of the following is true?

The average change in parade attendance is an additional 191 people per one-degree increase in temperature.

The National Football League has performed a study in which the total yards gained by teams in games was used as an independent variable to explain the variation in total points scored by teams during games. The points scored ranged from 0 to 57 and the yards gained ranged from 187 to 569. The following regression model was determined: y^ = 12.3 + .12x Given this model, which of the following statements is true?

The average change in points scored for each increase of one yard will be 0.12

Use the following regression results to answer the question below.

The correlation between x and y must be approximately -0.8851.

A bank is interested in determining whether its customers' checking balances are linearly related to their savings balances. A sample of n = 20 customers was selected and the correlation was calculated to be +0.40. If the bank is interested in testing to see whether there is a significant linear relationship between the two variables using a significance level of 0.05, the value of the test statistic is approximately t = 1.8516.

True

A study was recently done in which the following regression output was generated using Excel. chapter 14a.jpg Given this output, we would reject the null hypothesis that the population regression slope coefficient is equal to zero at the alpha = 0.05 level.

True

Given a sample of data for use in simple linear regression, the values for the slope and the intercept are chosen to minimize the sum of squared errors.

True

If it is known that a simple linear regression model explains 56 percent of the variation in the dependent variable and that the slope on the regression equation is negative, then we also know that the correlation between x and y is approximately -0.75.

True

If the correlation coefficient for two variables is computed to be a -0.70, the scatter plot will show the data to be downward sloping from left to right.

True

In a university statistics course a correlation of -0.8 was found between numbers of classes missed and course grade. This means that the fewer classes students missed, the higher the grade.

True

State University recently randomly sampled ten students and analyzed grade point average (GPA) and number of hours worked off-campus per week. The following data were observed: GPA HOURS 3.14 25 2.75 30 3.68 11 3.22 18 2.45 22 2.80 40 3.00 15 2.23 29 3.14 10 2.90 0 In this study the independent variable is the number of hours worked off campus per week

True

The following regression model has been computed based on a sample of twenty observations: = 34.2 + 19.3x. Given this model, the predicted value for y when x = 40 is 806.2.

True

The scatter plot is a two dimensional graph that is used to graphically represent the relationship between two variables.

True

When a pair of variables has a positive correlation, the slope in the regression equation will always be positive.

True

You are given the following sample data for two variables: YX 10 100 8 110 12 90 15 200 16 150 10 100 10 80 8 90 12 150 The sample correlation coefficient for these data is approximately r = 0.755.

True

Which of the following statements is correct?

Two variables that are uncorrelated with one another may still be related in a nonlinear manner.