1. Based on experience, it is believed that there is a relationship between a laser measurement device operating on the device's battery level, the number of previous uses, and the idle time before measurement. The following measurements were taken (* to the current values of columns 2 and 4 add # group / 10 and to column 3 subtract # group / 10)

a) Is the multiple regression model a good model? Determine if a significance below 0.1 is possible with which it is a good model and another with which it is not. In case of being a good model, what is the probability that the device will work if the battery level is 56.1, the number of previous uses is 36.1 and 3.3 hours on standby? Repeat the exercise, if the variables in columns 2 to 4 are taken the natural logarithm.

b) For each of the models between the linear, exponential, logarithmic and potential models, to explain possible connections between the variables "battery level" and "number of uses", construct the scatter diagram to which the graph of the respective model, and then do the hypothesis test to determine whether or not there is a correlation between the variables. For this, it is necessary to determine in each model a level of significance with which there is or is not correlation. Show an example of the use of models if they are good models, and how to forecast if they are not

Works the device 1 1 0 1 1 1 0 0 1 1 1 1 Current level History of Of battery usage in thousands 87.8 25.0 91.2 12.6 16.6 45.2 56.4 33.5 61.7 29.3 79.2 25.4 14.3 57.1 18.0 62.8 29.3 40.1 100.0 3.3 62.2 18.7 Hours history average resting 4.5 6.0 0.8 2.6 3.1 4.2 1.2 1.8 2.4 6.6 3.4 Works the device 1 1 0 1 1 1 0 0 1 1 1 1 Current level History of Of battery usage in thousands 87.8 25.0 91.2 12.6 16.6 45.2 56.4 33.5 61.7 29.3 79.2 25.4 14.3 57.1 18.0 62.8 29.3 40.1 100.0 3.3 62.2 18.7 Hours history average resting 4.5 6.0 0.8 2.6 3.1 4.2 1.2 1.8 2.4 6.6 3.4