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In: Statistics and Probability

Use Minitab and produce the appropriate output to answer the following questions. Attach or include the...

Use Minitab and produce the appropriate output to answer the following questions. Attach or include the relevant Minitab output.

  1. Construct a scatter plot. Recalling what scatter plots are used for, write a couple of sentences addressing what you observed from the plot. Be sure to relate your observations to the purpose of using scatter plots in regression. (4 points)
  2. Can we conclude that median family income helps in predicting median home price? Follow the 7 steps for hypothesis testing. (10 points)
  3. Find the sample regression equation and interpret the coefficients. Remember your interpretations should be in terms of the problem. (4 points)
  4. Find the coefficient of determination, and interpret its value. (3 points)
  5. Use residual analysis to check the validity of the model and fully explain your findings and conclusions. (6 points)
  6. Estimate with 95% confidence the average median home price for all families with a median income of $45,000. Predict with 95% confidence the estimated median home price for an individual family with a median income of $45,000. Write at least one sentence using your confidence interval and at least one sentence using your prediction interval. (6 points)
  7. Verify that the p-value for the F is the same as the slope’s t statistic’s p-value, and show that t2 = F. (3 points)
  8. Attach or include the relevant Minitab output. (6 points)
    Income and Home Prices in U.S. States (n = 51)
    State X = Income Y = MedPrice AvPrice
    AK 40933 241750 263931
    AL 57848 128969 153099
    AR 46896 120560 139124
    AZ 38587 147669 182553
    CA 54283 330037 391609
    CO 60233 217558 267924
    CT 65998 266845 341436
    DC 55214 404380 506654
    DE 56928 216902 247793
    FL 44066 144501 183843
    GA 44117 129446 159657
    HI 59539 499837 587760
    IA 47050 118036 139543
    ID 50728 140436 164999
    IL 46139 152387 186308
    IN 49016 113416 132068
    KS 46054 118687 135301
    KY 41104 130344 150614
    LA 39300 152413 171584
    MA 47931 306363 373062
    MD 64201 256411 292254
    ME 60934 175175 209697
    MI 46276 96398 116143
    MN 52321 164105 194336
    MO 38160 123754 147162
    MS 45817 126484 140317
    MT 41280 178188 206439
    NC 52504 154481 191255
    ND 51200 133473 147844
    NE 66633 120415 139325
    NH 62968 220625 254399
    NJ 45134 282633 325722
    NM 49781 161176 188610
    NV 43830 153364 179627
    NY 51006 245858 299812
    OH 45886 113730 132093
    OK 43103 118771 137614
    OR 50602 206977 234853
    PA 48314 153439 178266
    RI 51623 230354 269788
    SC 41698 135855 171514
    SD 45352 156243 175849
    TN 38591 123613 158176
    TX 47266 134854 160510
    UT 56701 194147 226030
    VA 55928 229420 268338
    VT 60367 203970 236773
    WA 56163 248555 284782
    WI 42777 153935 177864
    WV 50351 129369 150706
    WY 52201 183202 21112

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