Question

You probably regard your university education as an investment. You spend your valuable time, effort, and tuition fees and in return you obtain a degree. The provincial and federal governements also regard their funding of universities to be an investment. But is the investment equally effective in producing graduates across all provinces? The data bellow indicates the number of graduates at the bachelors, masters and doctorate levels and funding from four sources: Investment of university endowment funds, provincial funding, federal funding, tuition fees. Can we estimate the number of graduates from the level of these sources of funding? Does population size impact the equation? What other factors could influence results?

		Population size	Bachelors	Masters	Doctorate	Investment Income	Federal	Provincial	Tuition
1	Alberta	4,067,176	15720	3297	579	126680000	311184000	2110750000	798612000
2	British Columbia	4,631,000	16980	4488	393	136505000	352119000	2052199000	1021043000
3	Manitoba	1,282,000	5835	708	96	23152000	82805000	496334000	190402000
4	New Brunswick	753,915	4344	504	45	24377000	54219000	200677000	132086000
5	Newfoundland and Labrador	528,449	2760	531	51	3757000	61676000	292731000	72502000
6	Nova Scotia	942,927	7959	1716	111	32551000	98062000	359035000	318869000
7	Ontario	13,600,000	84714	13095	2049	438746000	1132905000	5010652000	3334466000
8	Prince Edward Island	146,284	660	48	9	2134000	17553000	63118000	35506000
9	Quebec	8,215,000	33438	9972	1428	136634000	745905000	4307043000	700697000
10	Saskatchewan	1,130,000	2979	435	63	45108000	108851000	589425000	176926000

Answer 1

The regression equation is defined as,

Where Y = Total graduates, X1 = Population size, X2 = Investment Income, X3 = Federal funding, X4 = Provincial funding, X5 = Tution fees

Under the Homoskedasticity assumption, the expected value of error term will be zero

Now, the regression analysis is done in excel by following steps

Step 1: Write the data values in excel. Where, the total gradualte is the sum of bachelors, masters and doctorate. The screenshot is shown below,

Step 2: DATA > Data Analysis > Regression > OK. The screenshot is shown below,

Step 3: Select Input Y Range: 'Total graduate' column, Input X Range: all the other columns then OK. The screenshot is shown below,

The result is obtained. The screenshot is shown below,

The regression equation is,

From the regression output summary, we can see that only the variable Provincial funding is significant at 10% significant level. All the other variables are not significant.

Explanatory variable	Coefficient	P-value		Significance level
Population size	0.00264127	0.68226144	>	0.1	Not significant
Investment Income	-5.416E-05	0.61981904	>	0.1	Not significant
Federal	0.00010337	0.06297012	<	0.1	Not significant
Provincial	-1.218E-05	0.1123386	>	0.1	Significant
Tuition	9.6499E-06	0.51307473	>	0.1	Not significant

Hence we can say that population doesnot impact the equation (insignificant variable in equation). Only the the variable Provincial funding impact the equation (statistically significant variable in equation)