In order to explore the relationship between the rotation speed ofa drill and the lifetime of the drill bit, engineers varied the rotation speed of the drill (60, 80, 100,120, and 140) and measured the lifetime of four bits (in thousands of holes drilled) at each of the five speeds. Prior to running a regression, you created a scatter plot and did correlation analysis. The output is below. Scalar Plot . With 9596 Prediction Ellipse Observe ' s 20 Correlation 41.625 60 _ p-Value . 32 What is the result of a hypothesis test 0- p = A- p g ? Reject the null hypothesis with a p-value of 0.0032. Conclude that the correlation is not equal to zero. Fail to reject the null hypothesis with a p-value of 0.0032. Conclude that the correlation is equal to zero. (9 Fail to reject the null hypothesis with a p-value of -0.625. Conclude that the correlation is equal to zero. (D) Reject the null hypothesis with a p-value of -0.625. Conclude that the correlation is not equal to zero. In the context of a simple linear regression, the prediction interval for a particular value will always be wider than the confidence interval for that same value. True B FalseIn order to explore the relationship between the rotation speed ofa drill and the lifetime of the drill bit, engineers varied the rotation speed of the drill (60,80, 100, 120, and 140) and measured the lifetime offour bits (in thousands of holes drilled) at each of the five speeds. You ran a regression on the data and jotted down a 95% prediction interval for a speed of 120: (223,507). What does it mean? If we repeat this experiment many times, 95% of the lifetimes of drill bits that are used at a speed of 120 will fall between 2,230 and 5,070. 95% of our predictions for drill bit lifetimes for drills being used at a speed of 120 will fall between 2,230 and 5,070. We are 95% confident that the lifetime for an individual drill bit being used at a speed of 120 will be between 2,230 and 5,070. @@0 We are 95% confident that the average lifetime for a drill bit being used at a speed of 120 is between 2,230 and 5,070. In order to explore the relationship between the rotation speed ofa drill and the lifetime of the drill bit, engineers varied the rotation speed of the drill (60, 80, 100, 120, and 140) and measured the lifetime of four bits (in thousands of holes drilled) at each of the five speeds. Prior to running a regression, you created a scatter plot and did correlation analysis. The output is below. Scan" Plot . With 95% Predicon Ellipse Observe ' s 20 Correlation 41625 eo- p-Value . 32 1 r 3.0 3.5 Which ofthe following statements is true? ([9 In general, as speed increases, drill bit lifetime stays the same There is no relationship between drill bit lifetime and speed (9 In general, as speed increases, drill bit lifetime increases (D) In general, as speed increases, drill bit lifetime decreases. In order to explore the relationship between the rotation speed ofa drill and the lifetime ofthe drill bit, engineers varied the rotation speed of the drill (60, 80, 100, 120, and 140) and measured the lifetime of four bits (in thousands of holes drilled) at each of the five speeds. The regression output is below. The SAS System The REG Procedure Model: MODEL'I Dependent Variable: lifetime Nunber of Observations Reed 20 Number of Observations Used 20 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 1 4.62400 4.62400 11.56 00032 Error 18 7.19800 0.39989 Corrected Total 19 11 .8200 Root MSE 0.63237 R~Square 0.3911 Dependent Mean 4.33000 Adj RSq 0.3573 Coeff Var 14.60433 Parameter Estimates Parameter Standard Variable DF Estimate Error tValue Pr>|t| Intercept 1 6.03000 0.51954 1161 <.0001 speed what is the estimated regression equation with hat on top equals x space minus o :iy :jy my>