AP StatsName______

Using Excell

  1. A researcher wants to know if there is a relationship between the number of shopping centers in a state and the retail sales (in billions $) of that state. A random sample of 8 states is listed below. After determining, via a scatter-plot, that the data followed a linear pattern, the regression line was found. Using the given data and the given regression output answer the following questions.
  1. Find the least squares line.
  2. Is this linear model a good fit? Explain.
  3. Can we assume the data is approximately normal? Explain.
  4. What is the slope? Interpret it.
  5. What is the y-intercept? Interpret it.
  6. What is the strength of the relationship.
  7. Find the residual for 700 shoppers.
  8. What is the coefficient of determination? Interpret it.
  9. Find the SSresid, SSTo, and se.
  1. Coffee is a leading export from several developing countries. When coffee prices are high, farmers often clear forest to plant more coffee trees. Below are five years’ data on prices paid to coffee growers in Indonesia and the percent of forest area lost in a national park that lies in a coffee-producing region.
  1. Find the least squares line.
  2. Is the linear model a good model to use? Explain.
  3. Can we assume the data is approximately normal? Explain.
  4. What is the slope? Interpret it.
  5. What is the y-intercept? Interpret it.
  6. What percent of the variation in percent of forest lost can be explained by the least squares line?
  7. What is the strength of the relationship?
  8. Find the residual for 54 cents per pound.
  9. Find the SSresid, SSTo, and se.

Answer the following parts for Questions 3-4 below.

  1. Find the least squares line.
  2. What is the slope? Interpret it.
  3. What is the y-intercept? Interpret it.
  4. What is the strength of the relationship.
  5. What is the coefficient of determination? Interpret it.
  6. Find the SSresid, SSTo, and se.
  1. A chemical company wants to study the effect of extraction time on the efficiency of an extraction process. They obtained a random sample of extraction times and the corresponding efficiency scores. The output from Excel is given below.

Regression Statistics
Multiple R / 0.864
R Square / 0.746
Std Error / 5.139
Obs / 15
Coefficients / Std Error / t Stat / P-value / Lower 95% / Upper 95%
Intercept / 39.022 / 4.173079 / 9.350943 / 3.9E-07 / 30.00684 / 48.03761
Time / 0.764 / 0.123639 / 6.178365 / 3.33E-05 / 0.496782 / 1.030995
  1. The following is output from Excel for regression analysis. The researcher wanted to predict the total cholesterol (mg/100ml) using weight (kg) as the predictor variable. Using the output, please answer the following questions?

SUMMARY OUTPUT

Regression StatisticsANOVA

Multiple R0.265293SourcedfSSMSF

R Square0.070381Regress110231102311.741

Standard Error76.65431Residual231351455875.8

Observations25Total24145377

CoeffStd Errt StatP-valueLower 95%Upper 95%

Intercept199.3085.822.3220.029421.77376.825

Weight 1.621.2291.3200.1999-0.9214.1656