Many urban regions have experienced rapid population growth over the last 10 years. It is expected that growth will continue over the next 10 years. This has resulted in many of the large grocery store chains building new stores. 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. 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 $ 4.68 $ 87 .50 5. 2: 90. 70 5.57 108. 60 5.37 94. 50 6.5 119. 60 4.9 42.30 4. 16 70.40 4.42 44. 40 6.18 106.90 10 4.96 54.80 11 5 . 28 109.00 3.43 92 .60 3. 66 49 . 60 . 80 102.00 5 .55 105 .80 3.38 53 .40 4.90 67.00 6. 04 127.90 5. 62 130.70 20 5.73 116.90 21 5.92 88. 70 22 4.54 43.00 152. 80 24 3.27 4.98 56.60 75 5.95 152.40 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. (Round the final answers to 3 decimal places.) Food Income Income 0.432 Size 0.869 0.239 a-2. Do you see any problems with multicollinearity? There is no multicollinearity. b-1. Determine the regression equation. (Round the final answers to 3 decimal places. Negative answer should be indicated by a minus sign.) Food = 2.668 @ + 0.007 @ Income + 0.337 @ Size b-2. Discuss the regression equation. (Round the final answer to 1 decimal place.) Another dollar of income leads to an |increased @ food bill of |652.5 @ cents. b-3. How much does an additional family member add to the amount spent on food? (Round the final answer to the nearest whole number.) Another member of the family adds $| 337 @ to the food bill.c-1. What is the value of Re? (Round the final answer to 3 decimal places.) R2 = 0.809 Can we conclude that this value is greater than 0? Test at a significance level of 0.05. Ho: B1 = B2 = 0 Hy: Not all Bj's = 0 c-2. State the decision rule. (Round the final answer to 2 decimal places.) Ho is rejected if F> 3.40 c-3. Compute the value of the test statistic. (Round the final answer to 2 decimal places.) F= 46.54 c-4. What is your decision regarding Ho? Reject Ho- There is not enough information to prove that not all the slopes are zero. d. Would you consider deleting either of the independent variables? There is no need to delete variables