Answer:
a)
i) 0.2
ii) 111.2
b)
Slope=3.7 shows that due to unit increase in ratings the cost of a dinner increases by 3.7 units.
c)
The correlation coefficient 0.54 shows that there is moderate positive relation between ratings and cost of a dinner
d)
slope=r(Sy/Sx).
Slope=0.54(20.57/3.01)
Slope=3.7
Step-by-step explanation:
a.
We are predicting the cost of dinner through rating and the estimated regression equation is
y^=0.2+3.7x.
Where y=cost of dinner and x=ratings
i)
y^=0.2+3.7x
For 0 rating, putting x=0 in above equation
y^ =0.2+3.7(0)
y^=0.2
ii)
y^=0.2+3.7x
For 30 rating, putting x=30 in above equation
y^ =0.2+3.7(30)
y^=0.2 +111
y^=111.2
b.
The regression equation y^=0.2+3.7x shows that slope is 3.7. Slope=3.7 shows that due to unit increase in ratings the cost of a dinner increases by 3.7 units.
c.
The correlation coefficient 0.54 shows that there is moderate positive relation between ratings and cost of a dinner. It means that as ratings increases the cost of a dinner also increases.
d.
We know that
slope=r(Sy/Sx).
We are given that correlation coefficient r is 0.54, standard deviation of cost of dinner Y is 20.57 and the standard deviation of ratings X is 3.01 .
r=0.54, Sy=20.57 and Sx=3.01.
Slope=0.54(20.57/3.01)
Slope=0.54*6.834
Slope=3.69
Thus, slope=3.7.
