Question

Regression Statistics
Multiple R	0.896755
R Square	0.80417
Adjusted R Square	0.767452
Standard Error	51.04855
Observations	20
ANOVA
	df	SS	MS	F	Significance F
Regression	3	171220.5	57073.49	21.90118	6.56E-06
Residual	16	41695.28	2605.955
Total	19	212915.8
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	427.1938	59.60143	7.167509	2.24E-06	300.8444	553.5432	300.8444	553.5432
Temp (deg)	-4.58266	0.772319	-5.93364	2.1E-05	-6.21991	-2.94542	-6.21991	-2.94542
Insulation (ins.)	-14.8309	4.754412	-3.11939	0.006606	-24.9098	-4.75196	-24.9098	-4.75196
Age (yrs)	6.101032	4.01212	1.52065	0.147862	-2.40428	14.60635	-2.40428	14.60635

1. For the slope coefficient of the variable with the smallest slope coefficient (ignore sign, use absolute value), test to see if the “a priori” expectation from part (a) is confirmed. Use alpha = 0.05

Priori= Heating cost will increase as daily temperature increases, Heating cost will decrease as the number of attic insulation increases and heating costs increase as the age of the furnace increases.

Answer 1

The heating cost will increase as daily temperature increases.

Rejected outright as the slope coefficient is negative which indicated a negative correlation instead of a positive correlation suggested by the "a priori".

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The heating cost will decrease as the number of attic insulation increases.

The slope is negative (-14.83). Let us check whether the negative value is statistically significant.

H0: the slope coefficient is zero
H1: the slope is non-zero

The P-value of the test is 0.006606 which is less than alpha = 0.05. So, at a 5% significance level, the null hypothesis is rejected i.e. the negative slope is statistically significant. So, the "a priori" gets support from the model.

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The heating costs increase as the age of the furnace increases.

The slope is positive (6.101). Let us check whether the negative value is statistically significant.

H0: the slope coefficient is zero
H1: the slope is non-zero

The P-value of the test is 0.147862 which is more than alpha = 0.05. So, at a 5% significance level, the null hypothesis cannot be rejected and the negative slope becomes statistically insignificant. So, the "a priori" does not get support.