Many regions in North and South Carolina and Georgia haveexperienced rapid population growth over the last 10 years. It isexpected that the growth will continue over the next 10 years. Thishas motivated many of the large grocery store chains to build newstores in the region. The Kelley’s Super Grocery Stores Inc. chainis no exception. The director of planning for Kelley’s SuperGrocery Stores wants to study adding more stores in this region. Hebelieves there are two main factors that indicate the amountfamilies spend on groceries. The first is their income and theother is the number of people in the family. The director gatheredthe following sample information.
| Family | Food | Income | Size |
| 1 | | $ | 4.14 | | $ | 73.98 | | 4 |
| 2 | | | 4.08 | | | 54.90 | | 2 |
| 3 | | | 5.76 | | | 138.86 | | 4 |
| 4 | | | 3.48 | | | 52.02 | | 1 |
| 5 | | | 4.20 | | | 65.70 | | 2 |
| 6 | | | 4.80 | | | 53.64 | | 4 |
| 7 | | | 4.32 | | | 79.74 | | 3 |
| 8 | | | 5.04 | | | 68.58 | | 4 |
| 9 | | | 6.12 | | | 165.60 | | 5 |
| 10 | | | 3.24 | | | 64.80 | | 1 |
| 11 | | | 4.80 | | | 138.42 | | 3 |
| 12 | | | 3.24 | | | 125.82 | | 1 |
| 13 | | | 7.17 | | | 77.58 | | 7 |
| 14 | | | 5.94 | | | 146.51 | | 6 |
| 15 | | | 6.60 | | | 162.69 | | 8 |
| 16 | | | 5.40 | | | 141.30 | | 3 |
| 17 | | | 6.00 | | | 36.90 | | 5 |
| 18 | | | 5.40 | | | 56.88 | | 4 |
| 19 | | | 3.36 | | | 71.82 | | 1 |
| 20 | | | 4.68 | | | 69.48 | | 3 |
| 21 | | | 4.32 | | | 54.36 | | 2 |
| 22 | | | 5.52 | | | 87.66 | | 5 |
| 23 | | | 4.56 | | | 38.16 | | 3 |
| 24 | | | 5.40 | | | 43.74 | | 7 |
| 25 | | | 6.71 | | | 59.83 | | 5 |
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1. Develop a correlation matrix. (Round your answers to3 decimal places. Negative amounts should be indicated by a minussign.)
2. Determine the regression equation. (Round your answerto 3 decimal places.)
The regression equation is: Food = ____ + _____ income + _____size
3. How much does an additional family member add to theamount spent on food? (Round your answer to the nearest dollaramount.)
Another member of the family adds _________ to the foodbill.
4. What is the value ofR2?
5. Complete the ANOVA (Leave no cells blank - be certainto enter "0" wherever required. Round SS, MS to 4decimal places and F to 2 decimal places.)
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| | Source | DF | SS | MS | F | p-value | | Regression | | | | | | | Error | | | | | | | Total | | | | |
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6. State the decision rule for 0.05 significance level.H0: = ?1 = ?2 = 0;H1: Not all ?i's = 0.
7. Complete the table given below. (Leave no cells blank- be certain to enter "0" wherever required. Round Coefficient, SECoefficient, P to 4 decimal places and T to 2decimal places.)
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| | Predictor | Coefficient | SE Coefficient | t | p-value | | Constant | | | | | | Income | | | | | | Size | | | | |
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