An energy consultant investigates the relationship between the average daily outdoor temperature, TTT (∘C^{\circ}\text{C}∘C), and the daily gas consumption, GGG (m3m^3m3), for a sample of 20 residential homes during the winter.
The following summary statistics were recorded:
STT=450STG=−315∑G=160∑T=220∑G2=1536 S_{TT} = 450 \quad S_{TG} = -315 \quad \sum G = 160 \quad \sum T = 220 \quad \sum G^2 = 1536 STT=450STG=−315∑G=160∑T=220∑G2=1536Show that the product moment correlation coefficient (PMCC) for these data is −0.928-0.928−0.928 to 3 significant figures.
A scatter diagram of GGG against TTT is drawn. State two features of the scatter diagram you would expect to see based on the PMCC value.
Calculate the equation of the regression line of GGG on TTT in the form G=a+bTG = a + bTG=a+bT. Give the values of aaa and bbb to 3 significant figures.
Interpret the value of the gradient of this regression line within the context of the study.
The consultant decides to adjust the temperature data by dividing all TTT values by 2 to analyze the readings relative to a different reference scale.
State, for each of the following, whether the value would increase, decrease, or stay the same as a result of this change: (i) the product moment correlation coefficient, (ii) the magnitude of the gradient of the regression line, (iii) the GGG-intercept of the regression line.
