the data jigsaw is below the question

Date Title Publisher Dimension Pieces Time 1/15/11 Minneapolis The Great , 2D 550 270 1/13/12 The Dog USAopoly 2D 550 753 7/8/12 Alpine Cast Wrebbit 3D 1000 1118 6/3/13 Graceland Wrebbit 3D 460 314.0833 1/26/14 Animal Are The Round 2D 700 560.0167 8/15/15 Japanese (SunsOut 2D 1000 943.0333 7/31/17 The Old M& Wrebbit 3D 426 348.2667 8/7/17 Antique GicBuffalo Gar 3D 530 742.8 1/7/18 The Eight li SunsOut 2D 1000 1332.133 1/16/18 Rock Wall : SunsOut 2D 300 149.8 2/12/18 Night View, SunsOut 2D 500 309.1667 7/14/18 Brooklyn, MSure-Lox 2D 500 221.6 7/28/18 Lake Garda Sure-Lox 2D 750 489.2333 8/1/18 Rhododenc Sure-Lox 2D 500 241.9 8/10/18 Trolle-Ljung Sure-Lox 2D 750 350.1167 9/26/18 Castle Dre: Buffalo Gar 2D 2072 2899.45 1/31/19 The Great ' Beverly 2D 1000 2565.667 3/22/19 Basin Retre Sure-Lox 2D 500 228.6167 5/31/19 Yokohama, Sure-Lox 2D 300 108.65 8/10/19 You're Eve Hallmark 2D 70 19.5 8/8/19 A Very Mer Jumbo 2D 1000 923.45 8/14/19 Little India, Sure-Lox 2D 1000 546.5167 8/23/19 Taj Mahal Wrebbit 3D 1077 926.9667 9/21/19 M&M's Puz USAopoly 2D 504 810.0833 11/2/19 European (Sure-Lox 2D 300 170.4 11/12/19 Neuschwar Sure-Lox 2D 500 389.45 1/21/20 Thatchet C Sure-Lox 2D 1000 1182.817 2/24/20 Lakeside NV Ceaco 2D 1000 1013 4/9/20 The Aspen Ceaco 2D 302 137.5667 4/19/20 Mount Bak Sure-Lox 2D 500 298.5667 5/23/20 A Light in th Ceaco 2D 302 122 6/6/20 The Sea of Ceaco 2D 500 429.3167 8/28/20 Quilt Block: Cobble Hill 2D 2000 1180.6 1/9/21 Rainbow Cobble Hill 2D 2000 1814.65 1/21/21 Blazing with NA 2D 986 384.4833 2/7/21 Chateau de Sure-Lox 2D 1000 998.45 3/13/21 Minnesota Big Stick S12D 107 130.8333In Chapter 3 of the lecture notes, Tony mentioned that he has solved a total of 36 jigsaw puzzles. Earlier in March 2021, Tony had solved a 37th jigsaw puzzle. The updated dataset is given as jigsaw new. csv. The data file contains the following variables: Time Solving time (in minutes) Pieces Number of pieces of the puzzle Dimension A binary categorical variable indicating whether the puzzle is 2D or 3D1. [2 pts] Fit the model m3 given by the formula log (Time) ~ log (Pieces) * Dimension and obtain the model summary using the summary () function. Remember to attach your R input and output. 2. [3 pts] Based on model m3, what is the estimated regression line for log (Time) ~ log (Pieces) for 2D and 3D puzzles, respectively? Your answers should be in the form Ellog(Time) | Pieces = x, Dimension = 2D]= log (x) Ellog(Time) | Pieces = x, Dimension = 3D] = log (x). 3. [3 pts] The 3D jigsaw puzzle "US Capitol" produced by Wrebbit has 764 pieces. Give a point estimate for the number of minutes it would take for Tony to complete that jigsaw puzzle. 4. [3 pts] Do you think we can simplify separate regression lines model m3 for log (Time) on log (Pieces) and Dimension into a parallel regression lines model? Use an appropriate statistical test to answer this question. Use the significance level 0.05. Remember to attach your R input and output if you have used any additional R codes. Q5 [2 pts] Use the command hatvalues (m3) to obtain the leverages of each dataset. How many leverage points are there in the dataset? Remember the cutoff threshold for multiple linear regression models is 2(+1) " , where p is the number of parameters EXCLUDING the intercept