Studies have shown that the frequency with which shoppers browse Internet retailers is positively correlated to the frequency with which they actually make purchases.
The following data show respondents age and "How many minutes do you browse online retailers per year?”
Age (X) Time (Y)
16 470
17 319
19 365
22 387
22 293
22 509
22 464
28 274
28 431
28 462
28 626
30 383
33 601
34 598
35 676
35 571
35 612
36 749
39 693
39 505
40 716
42 603
43 509
44 575
48 609
50 557
50 662
51 760
52 428
54 616
58 702
59 775
60 750
10 Compute the correlation between Age and Time using Data Analysis. Include the labels in the Input Range and check the Labels checkbox.
11 Compute the correlation using the Excel function =CORREL. If answers for #10 and 11 do not agree, there is an error.
12 The strength of the correlation motivates further examination.
a) Make a scatter plot linked to and near the data above, and with Age on the horizontal (X) axis.
b) Add to your chart
A meaningful title
Vertical axis label Time
Horizontal axis label Age
c) Complete the chart by adding Trendline and checking boxes
13 Read directly from the chart:
a) Intercept =
b) Slope =
c) R2 =
14a Perform regression using Data Analysis. Select the Time data first, include the labels in row 4 in the Input Range, and check the Labels checkbox.
14b In the Regression output, highlight the Y-intercept red, the slope blue, and R2 green.
15 Use the Data Analysis output to predict the number of minutes spent by a 35-year old shopper. Enter = followed by the regression formula,
entering the intercept and slope into the formula by clicking on the corresponding cells in the regression output.
(Week 11 Presentation, slide 11)
16 Is it appropriate to use this data to predict the amount of time that a 75-year-old will spend browsing online retailers ?
Why or why not (Week 11 Presentation, slide 8)?
Analyzing Correlation and Regression between Age and Time Spent Browsing Online Retailers
Introduction
Studies have suggested a positive correlation between the frequency of browsing online retailers and the frequency of making purchases. In this analysis, we will examine the relationship between respondents' age and the number of minutes they spend browsing online retailers per year. By calculating the correlation and performing regression analysis, we aim to understand the strength of the relationship and predict the time spent by shoppers based on their age.
Data Analysis
10. Correlation Calculation: We will compute the correlation between age and time spent browsing online retailers using Excel's Data Analysis tool, ensuring to include labels in the input range.
11. Correlation Check: Additionally, we will calculate the correlation using the =CORREL function in Excel to verify the accuracy of the computed correlation.
Correlation Results
- If the correlation values from the Data Analysis and Excel function do not agree, it indicates an error in the calculation.
12. Scatter Plot Visualization:
- Create a scatter plot with Age on the horizontal (X) axis and Time on the vertical (Y) axis, linked to the provided data.
- Customize the chart with appropriate labels, title, and add a trendline for further analysis.
Scatter Plot Analysis
- a) Intercept: Determine the intercept value from the trendline equation.
- b) Slope: Identify the slope value from the trendline equation.
- c) R-squared (R²): Calculate the coefficient of determination to assess the goodness of fit of the regression line.
14. Regression Analysis:
- Perform regression analysis using Excel's Data Analysis tool by selecting the Time data and ensuring to include labels in the input range.
Regression Output
- Highlight key results in different colors for clarity:- Y-intercept in red
- Slope in blue
- R-squared value in green
15. Prediction Calculation:
- Utilize the regression formula to predict the number of minutes spent by a 35-year-old shopper based on the intercept and slope values obtained from the regression output.
16. Prediction Accuracy:
- Evaluate if it is appropriate to use this data to predict the time a 75-year-old shopper will spend browsing online retailers based on statistical reasoning.
Conclusion
By conducting correlation and regression analyses on age and time spent browsing online retailers, we can gain insights into the relationship between these variables and make predictions regarding shoppers' behavior. The results of this analysis will provide valuable information for understanding customer preferences and optimizing online retail experiences based on demographic factors like age.