Many regions in North and South Carolina and Georgia have experienced rapid population growth over the last 10 years. It is expected that the growth will continue over the next 10 years. This has motivated many of the large grocery store chains to build new stores in the region. The Kelley’s Super Grocery Stores Inc. chain is no exception. The director of planning for Kelley’s Super Grocery Stores wants to study adding more stores in this region. He believes there are two main factors that indicate the amount families spend on groceries. The first is their income and the other is the number of people in the family. The director gathered the following sample information. Family Food Income Size 1 $ 5.04 $ 73.98 4 2 4.08 54.90 2 3 5.76 94.14 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 6.60 77.58 7 14 4.92 171.36 2 15 6.60 82.08 9 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 4.80 48.42 5 Food and income are reported in thousands of dollars per year, and the variable size refers to the number of people in the household. a-1. Develop a correlation matrix. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.) a-2. Do you see any problems with multicollinearity? b-1. Determine the regression equation. (Round your answers to 3 decimal places.) b-2. How much does an additional family member add to the amount spent on food? (Round your answer to the nearest dollar amount.) c-1. What is the value of R2? (Round your answer to 3 decimal places.) c-2. Complete the ANOVA. (Leave no cells blank - be certain to enter "0" wherever required. Round SS, MS to 4 decimal places and F to 2 decimal places.) c-3. State the decision rule for 0.05 significance level. H0: = β1 = β2 = 0; H1: Not all βi's = 0. (Round your answer to 2 decimal places.) c-4. Can we reject H0: = β1 = β2 = 0? d-1. Complete the given below table. (Leave no cells blank - be certain to enter "0" wherever required. Round Coefficient, SE Coefficient, p-value to 4 decimal places and t to 2 decimal places.) d-2. Would you consider deleting either of the independent variables?
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
Many regions in North and South Carolina and Georgia have experienced rapid population growth over the last 10 years. It is expected that the growth will continue over the next 10 years. This has motivated many of the large grocery store chains to build new stores in the region. The Kelley’s Super Grocery Stores Inc. chain is no exception. The director of planning for Kelley’s Super Grocery Stores wants to study adding more stores in this region. He believes there are two main factors that indicate the amount families spend on groceries. The first is their income and the other is the number of people in the family. The director gathered the following sample information.
| Family | Food | Income | Size | |||||
| 1 | $ | 5.04 | $ | 73.98 | 4 | |||
| 2 | 4.08 | 54.90 | 2 | |||||
| 3 | 5.76 | 94.14 | 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 | 6.60 | 77.58 | 7 | |||||
| 14 | 4.92 | 171.36 | 2 | |||||
| 15 | 6.60 | 82.08 | 9 | |||||
| 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 | 4.80 | 48.42 | 5 | |||||
Food and income are reported in thousands of dollars per year, and the variable size refers to the number of people in the household.
a-1. Develop a
a-2. Do you see any problems with multicollinearity?
b-1. Determine the regression equation. (Round your answers to 3 decimal places.)
b-2. How much does an additional family member add to the amount spent on food? (Round your answer to the nearest dollar amount.)
c-1. What is the value of R2? (Round your answer to 3 decimal places.)
c-2. Complete the ANOVA. (Leave no cells blank - be certain to enter "0" wherever required. Round SS, MS to 4 decimal places and F to 2 decimal places.)
c-3. State the decision rule for 0.05 significance level. H0: = β1 = β2 = 0; H1: Not all βi's = 0. (Round your answer to 2 decimal places.)
c-4. Can we reject H0: = β1 = β2 = 0?
d-1. Complete the given below table. (Leave no cells blank - be certain to enter "0" wherever required. Round Coefficient, SE Coefficient, p-value to 4 decimal places and t to 2 decimal places.)
d-2. Would you consider deleting either of the independent variables?
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