Exam 12: Simple Linear Regression

A company has recorded data on the daily demand for its product (y in thousands of units) and the unit price (x in hundreds of dollars). A sample of 11 days demand and associated price resulted in the following data. a.Using the above information, develop the least-squares estimated regression line. b.Compute the coefficient of determination. c.Perform an F test and determine whether or not there is a significant relationship between demand and unit price. Let   0.05. d.Perform a t test to determine whether the slope is significantly different from zero. Let   0.05. e.Would the demand ever reach zero? If yes, at what price would the demand be zero. Show your complete work.

If the coefficient of determination is 0.81, the coefficient of correlation

The difference between the observed value of the dependent variable and the value predicted by using the estimated regression equation is the

A regression analysis between demand (y in 1000 units) and price (x in dollars) resulted in the following equation  9  3x The above equation implies that if the price is increased by $1, the demand is expected to

If the coefficient of correlation is a positive value, then the slope of the regression line

If the coefficient of correlation is 0.8, the percentage of variation in the dependent variable explained by the estimated regression equation is

In a regression analysis, the variable that is being predicted

Compared to the confidence interval estimate for a particular value of y (in a linear regression model), the interval estimate for an average value of y will be

In a residual plot against x that does not suggest we should challenge the assumptions of our regression model, we would expect to see

We are interested in determining the relationship between daily supply (y) and the unit price (x) for a particular item. A sample of ten days supply and associated price resulted in the following data. a.Develop the least square estimated regression equation. b.Compute the coefficient of determination and fully explain its meaning. c.At   0.05, perform a t-test and determine if the slope is significantly different from zero.

Exhibit 12-6 You are given the following information about y and x. -Refer to Exhibit 12-6. The least squares estimate of b₁ equals

Assume you have noted the following prices for books and the number of pages that each book contains. a.Develop a least-squares estimated regression line. b.Compute the coefficient of determination and explain its meaning. c.Compute the correlation coefficient between the price and the number of pages. Test to see if x and y are related. Use  = 0.10.

Part of an Excel output relating X (independent variable) and Y (dependent variable) is shown below. Fill in all the blanks marked with "?".

Exhibit 12-3 Regression analysis was applied between sales data (in $1,000s) and advertising data (in $100s) and the following information was obtained. -Refer to Exhibit 12-3. The critical F value at   0.05 is

If there is a very strong correlation between two variables, then the coefficient of correlation must be

Given below are seven observations collected in a regression study on two variables, x (independent variable) and y (dependent variable). Use Excel's Regression Tool to construct a residual plot and use it to determine if any model assumption have been violated.

A regression analysis between sales (y in $1000) and advertising (x in dollars) resulted in the following equation  50,000 + 6x The above equation implies that an

Shown below is a portion of a computer output for a regression analysis relating supply (Y in thousands of units) and unit price (X in thousands of dollars). a.What has been the sample size for this problem? b.Perform a t test and determine whether or not supply and unit price are related. Let  = 0.05. c.Perform and F test and determine whether or not supply and unit price are related. Let  = 0.05. d.Compute the coefficient of determination and fully interpret its meaning. Be very specific. e.Compute the coefficient of correlation and explain the relationship between supply and unit price.f. Predict the supply (in units) when the unit price is $50,000.

A company has recorded data on the weekly sales for its product (y) and the unit price of the competitor's product (x). The data resulting from a random sample of 7 weeks follows. Use Excel's Regression Tool to construct a residual plot and use it to determine if any model assumption have been violated.

Exhibit 12-3 Regression analysis was applied between sales data (in $1,000s) and advertising data (in $100s) and the following information was obtained. -Refer to Exhibit 12-3. Based on the above estimated regression equation, if advertising is $3,000, then the point estimate for sales (in dollars) is