Question

# Use regression analysis to examine the variation in a dependent variable.  Use 0.05 level of significance unless...

Use regression analysis to examine the variation in a dependent variable.  Use 0.05 level of significance unless other stated.

• When doing various tests (fit, significance) report the relevant values of the parameters (test stats, R square)
• Make sure to write out your hypotheses and rejection rules for significance tests.  If p-values are greater than 0 report the level at which your test is significant.
• Conclusions are to be in terms of the problems; pretend the reader has no idea about you were asked to do.
• Do not include the confidence interval data in your report (will fit the page better)

Sunflower Clothing Chain

3.   Sales for Sunflowers, a clothing chain, have increased during the past 12 years as the chain expanded the number of stores open.  Until now, Sunflowers’ senior managers selected sites based on subjective factors.  As the new director of planning, you will need to develop a systematic approach to selecting new sites.  This plan must be able to forecast annual sales for all potential stores under consideration.  You believe that the size of the store significantly contributes to the success of a store and want to use this relationship in the decision-making process.

Examine the relationship between the store size (thousands of square feet) and its annual sales (in million dollars) for Sunflowers women's clothing chain.

• Identify the regression equation.
• Interpret slope coefficient and test its significance.
• How well does the equation fit the data?
• Does the equation significantly explain the relationship between Sunflower's annual sales and the size of its stores?
 SUMMARY OUTPUT Regression Statistics Multiple R 0.85 R Square 0.73 Adjusted R Square 0.71 Standard Error 1.69 Observations 14.00 ANOVA df SS MS F Significance F Regression 1 92.34 92.34 32.26 0.00 Residual 12 34.34 2.86 Total 13 126.68 Coefficients Standard Error t Stat P-value Intercept 1.02 0.92 1.11 0.29 Square Feet (000) 1.56 0.27 5.68 0.00

• Identify the regression equation.

y = 1.02 + 1.56*x

• Interpret slope coefficient and test its significance.

For every square foot, sales will increase by 1.56.

The hypothesis being tested is:

H0: β1 = 0

H1: β1 ≠ 0

The p-value is 0.00.

Since the p-value (0.00) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that the slope is significant.

• How well does the equation fit the data?

0.73 = 73% of the variation in the model is explained. This is a good fit.

• Does the equation significantly explain the relationship between Sunflower's annual sales and the size of its stores?

Yes

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