Chapter 5.1, Problem 1E

To determine

To Find: The graph of the linear regression equation for the given data and determine the equation that is better fit for the data.

Answer to Problem 1E

The required linear regression equation and the quadratic equation s are $h\left(t\right)=19.2t+1.92$ and $h\left(t\right)=-16t^2+32t$ . The graph of the linear regression is shown in Figure 10 and quadratic regression is shown in Figure 18.

Explanation of Solution

Given:

The given table is shown in Table 1

Table 1

Time	Height
0.1	3.04
0.2	5.76
0.3	8.16
0.4	10.24
0.5	12
0.6	13.44
0.7	14.90

Calculation:

Press the start button and enter the data as shown in Figure 1

  

Figure 1

Press the stat button and choose CALC as shown in Figure 2

  

Figure 2

Press enter and select 4 as shown in Figure 3

  

Figure 3

Press enter twice and the required linear regression is obtained as shown in Figure 4

  

Figure 4

Press the 2^nd key and then STAT PLOTS and select 1 as shown in Figure 5

  

Figure 5

Press the select type and mark as shown in Figure 6

  

Figure 6

Press zoom button and select the option 9 as shown in Figure 7

  

Figure 7

Press the graph button as shown in Figure 8

  

Figure 8

Press Y= button to obtain the linear regression as shown in Figure 9

  

Figure 9

Then , press the graph button as shown in Figure 10

  

Figure 10

Press the enter and then select the option 5 as shown in Figure 11

  

Figure 11

Press the button 2 two times and the required quadratic regression equation is obtained as shown in Figure 12

  

Figure 12

Press the 2^nd key and then STAT PLOTS and select 1 as shown in Figure 13

  

Figure 13

Press the select type and mark as shown in Figure 14

  

Figure 14

Press zoom button and select the option 9 as shown in Figure 15

  

Figure 15

Press the graph button as shown in Figure 16

  

Figure 16

Press Y= button to obtain the linear regression as shown in Figure 17

  

Figure 17

Then , press the graph button as shown in Figure 18

  

Figure 18

Thus, the required linear regression equation and the quadratic equation s are $h\left(t\right)=19.2t+1.92$ and $h\left(t\right)=-16t^2+32t$ . The graph of the linear regression is shown in Figure 10 and quadratic regression is shown in Figure 18.