Question

In: Statistics and Probability

Caption: Princess Foods wants to determine if there is a relationship in the amount a household...

Caption: Princess Foods wants to determine if there is a relationship in the amount a household spends on prepared foods to family size and income. Parthika: Well, we still have data collected from a previous marketing study. Let’s use that. We have an Excel file. I am sure we can find the spreadsheet. It should have the exact information we need. Liwei: Yes, this could be interesting. We may find enough evidence to rethink the meal preparation kits again. Bonnie: Great idea. We need to know it the data is a good fit and what the exact relationship is between the dependent variable and the independent variables. We can use this information to help us design perhaps a new line of prepared frozen foods. ParthikaYes, what about the prepackaged salad bowls. We really need to see this data. Bonnie: Yes, let’s get right on this.

Please use the below data and Excel to determine the equation that represents the relationship and explain the goodness of fit. Based on the data, write a memo and interpret the results. How might this data be used?

*Please show step by step how to complete regression analysis using the Data Analysis Toolpack in Excel.

Dollars spent on Prepared food Family size Gross monthly income
495.86 4 3126
642.77 5 3933
364.81 3 1925
619.3 5 3736
238.71 1 1453
378.94 2 2538
302.58 1 1798
231.74 2 1189
428.67 3 2247
286.99 3 1460
268.81 1 1567
329.81 2 1622
627.25 5 3828
421.52 3 2782
656.38 5 3978
400.64 3 2493
603.41 6 3753
560.69 4 3778
623 5 3609
416.12 2 2262
323.9 1 1966
418.78 3 2736
506.46 4 3274
552.53 2 3480
586.46 4 3741
637.18 8 3684
244.49 2 1476
507.19 5 2835
512.56 5 2873
312.89 1 1618
329.05 2 1565
243.49 2 1582
560.37 8 3380
599.9 5 3922
657.09 5 3845
394.82 2 2233
556.42 4 3098
596.05 8 3707
365.8 4 2071
489.08 3 3166

Solutions

Expert Solution

first go to data analysis tool pack and select regression

now,

select the input Y range (dollar spend on food)

input X range (family size , monthly income together)

and select a cell for output result

a summary will be displayed

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.980501
R Square 0.961383
Adjusted R Square 0.959295
Standard Error 27.83077
Observations 40
ANOVA
df SS MS F Significance F
Regression 2 713455.4 356727.7 460.5601 7.17E-27
Residual 37 28658.42 774.5519
Total 39 742113.8
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 61.42165 14.3251 4.287695 0.000124 32.39625 90.44706 32.39625 90.44706
Family size 9.693092 3.607685 2.68679 0.010742 2.383228 17.00296 2.383228 17.00296
Gross monthly income 0.132166 0.007535 17.5394 1.62E-19 0.116898 0.147434 0.116898 0.147434

so ,

dollar spend = 61.42165 + 9.693092*(family size) + 0.132166 * (income)

................

R2 =0.96138

it implies that there is 96.14% of data can be explained by the equation

also R = 98.05 , it represents the strong relationship between the dependent and independent variables

thanks

orchestra answered 2 years ago
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