You are part of a team investigating the identifying motorvehicle accidents. A multiple regression model is to be constructedto predict the number of motor vehicle accidents in a town per yearbased upon the population of the town, the number of recordedtraffic offenses per year and the average annual temperature in thetown.

Data has been collected on 30 randomly selected towns:

Number of motor vehicle accidents per year	Population (× 1000)	No. of recorded traffic offences (× 100)	Average temperature °F
355	181	29	78
490	257	56	82
597	441	34	81
475	50	95	81
922	495	102	82
736	38	165	81
305	167	25	84
1,128	378	191	78
745	369	86	76
476	237	63	84
143	100	4	84
203	118	21	79
909	489	106	78
410	210	39	77
642	138	131	81
847	308	138	82
604	418	40	77
719	194	132	78
350	319	8	84
327	70	61	76
1,038	259	192	78
756	299	115	81
635	440	40	79
796	283	131	85
301	64	56	81
135	26	26	79
639	31	150	81
325	210	13	77
441	43	98	79
522	370	26	82

a)Find the multiple regression equation using all threeexplanatory variables. Assume that X₁ is population,X₂ is number of recorded traffic offenses per year andX₃ is average annual temperature. Give your answers to 3decimal places.

y^ =  + population + no. traffic offences + averagetemp

b)At a level of significance of 0.05, the result of the F testfor this model is that the null hypothesis isis not rejected.

For parts c) and d), using the data, separately calculate thecorrelations between the response variable and each of the threeexplanatory variables.

c)The explanatory variable that is most correlated with numberof motor vehicle accidents per year is:

population
number of traffic offenses
average annual temperature

d)The explanatory variable that is least correlated with numberof motor vehicle accidents per year is:

population
number of traffic offenses
average annual temperature

e)The value of R² for this model, to 2 decimalplaces, is equal to

f)The value of s_e for this model, to 3 decimalplaces, is equal to

g)Construct a new multiple regression model by removing thevariable average annual temperature. Give your answers to 3 decimalplaces.

The new regression model equation is:

y^ =  + population + no. traffic offences

h)In the new model compared to the previous one, the value ofR² (to 2 decimal places) is:

increased
decreased
unchanged

i)In the new model compared to the previous one, the value ofs_e (to 3 decimal places) is:

increased
decreased
unchanged