The following sample data contains the number of years of ✓ Solved

The following sample data contains the number of years of college and the current annual salary for a random sample of heavy equipment salespeople. Answer the questions with Excel formula by using the following numbers:

  1. Which variable is the dependent variable? Which is the independent variable?

  2. Determine the least squares estimated regression line.

  3. Draw the scatter plot and trendline.

  4. Test if the relationship between years of college and income is statistically significant at the .05 level of significance.

  5. Calculate the coefficient of determination.

  6. Calculate the sample correlation coefficient between income and years of college. Interpret the value you obtain.

The marketing department of a company has designed three different boxes for its product. It wants to determine which box will produce the largest amount of sales. Each box will be test-marketed in five different stores for a period of a month. Below you are given the information on sales. Answer the questions with Excel formula by using the following numbers:

  1. State the null and alternative hypotheses.

  2. Construct an ANOVA table.

  3. What conclusion do you draw?

The following data show the results of an aptitude test (Y) and the GPA grade point average of 10 students who want admission to a prestigious college:

  1. Plot the scatter diagram and insert the trendline.

  2. Develop a least square estimated regression line.

  3. Compute the coefficient of determination and comment on the strength of the regression relationship.

  4. Compute the correlation coefficient.

  5. Is the slope significant? Use a t-test and let α = 0.05.

Paper For Above Instructions

In this assignment, we will analyze three datasets related to different business scenarios, using Excel to perform statistical analysis and derive insights that can inform business decision-making.

Part 1: Heavy Equipment Salespeople

In the first dataset, we examine the relationship between the years of college education and the annual income of heavy equipment salespeople. The dependent variable in this case is the annual income, while the independent variable is the years of college.

To find the least squares estimated regression line, we run a regression analysis in Excel using the formula LINEST(y_values, x_values, TRUE, TRUE). This produces the regression equation in the format:

Income = m * (Years of College) + b

Where m is the slope and b is the y-intercept. Using Excel's regression output, we can extract these values directly from the regression analysis.

Next, we plot the scatter diagram using the data points along with the trendline to visualize the relationship. We can perform this by selecting the scatter plot option in Excel, and then adding a linear trendline to it.

To assess the significance of the relationship at the 0.05 level, we analyze the p-value associated with the variable in our regression output. If the p-value is less than 0.05, we reject the null hypothesis that states there is no relationship between the years of college and income.

Additionally, we compute the coefficient of determination (R²) using the output from our regression analysis, which reveals the proportion of variance in income explained by years of college. Furthermore, we calculate the sample correlation coefficient using the formula CORREL(array1, array2) to quantify the strength and direction of the linear relationship between these two variables. Values closer to +1 indicate a strong positive correlation.

Part 2: Marketing Department Sales Testing

In the second dataset, we will determine which of three different product boxes yields the highest sales. Our null hypothesis (H₀) posits that there is no significant difference in sales among the three boxes, while the alternative hypothesis (H₁) states that at least one box differs in sales.

To analyze the data, we conduct an ANOVA test. Using Excel, an ANOVA table can be constructed by navigating to the Data Analysis Toolpak and selecting ANOVA: Single Factor. This table will summarize the sources of variance among the groups.

After running the ANOVA test, we check the F-statistic and the associated p-value. If the p-value is less than 0.05, we reject H₀ and conclude that there is a significant difference in sales among the boxes. If not, we fail to reject H₀.

Part 3: Aptitude Test Scores and GPAs

The final examination involves an analysis of the relationship between aptitude test scores (dependent variable) and GPA (independent variable) as the students aspire to gain admission into a prestigious college.

We start by plotting a scatter diagram of the data points and adding a trendline to visualize the correlation. Following this, we build the least squares estimated regression line with a similar approach as previously described.

To measure the strength of the regression relationship, we compute the coefficient of determination (R²) using Excel. A high R² close to 1 implies a strong predictive ability of GPA on aptitude score results.

Next, we calculate the correlation coefficient using the formula mentioned above. This will provide a clear understanding of the relationship between GPA and aptitude scores. Finally, to test if the slope of our regression line is statistically significant, we perform a t-test, with a significance level of α = 0.05. A significant result would further validate our model.

Conclusion

In summary, statistical analysis through regression, ANOVA, and correlation coefficients provides powerful insights into business decision-making. The use of Excel facilitates these calculations and allows for a visual comparison of datasets, honing in on critical areas needing consideration in operational strategies.

References

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