So confused about formulas and if there is a calculator online to input- can you
ID: 3262398 • Letter: S
Question
So confused about formulas and if there is a calculator online to input- can you help? thank you a million times!
A candy bar manufacturer is interested in trying to estimate how sales are influenced by the price of their product. To do this, the company randomly chooses 6 small cities and offers the candy bar at different prices. Using candy bar slaes as the dependent variabe, the company will conduct a simple linear regression on the data below:
regression statistics
observations=6
ANOVA dof SS MS F sifnificance F
regression 1 3855.422 3855.422 14.51346 .018946
residual 4 1062.578 265.6446
total 5 4918
coefficients Error t stat p-value lower 95% Upper 95%
intercept 161.3855 26.16069 -6.16901 .003506 88.75183 234.0193
Price ($) -48.1928 12.65017 -3.80965 .018946 -83.3153 -13.0703
a) referring to the info above, what is the estimated slope for the candy bar price and sales data?
b) what is the estimated Y-intercept for the candy bar price and sales data?
c)what is the coefficicent of correlation for these data?
d) what is the perentage of the total variation in candy bar sales explained by the regression model?
e) if the price of the candy bar is set at $2, what is the predicted sales to be?
Explanation / Answer
Answer:
So confused about formulas and if there is a calculator online to input- can you help? thank you a million times!
A candy bar manufacturer is interested in trying to estimate how sales are influenced by the price of their product. To do this, the company randomly chooses 6 small cities and offers the candy bar at different prices. Using candy bar sales as the dependent variable, the company will conduct a simple linear regression on the data below:
regression statistics
observations=6
ANOVA dof SS MS F significance F
regression 1 3855.422 3855.422 14.51346 .018946
residual 4 1062.578 265.6446
total 5 4918
coefficients Error t stat p-value lower 95% Upper 95%
intercept 161.3855 26.16069 -6.16901 .003506 88.75183 234.0193
Price ($) -48.1928 12.65017 -3.80965 .018946 -83.3153 -13.0703
a) referring to the info above, what is the estimated slope for the candy bar price and sales data?
estimated slope = -48.1928
b) what is the estimated Y-intercept for the candy bar price and sales data?
estimated Y-intercept = 161.3855
c)what is the coefficient of correlation for these data?
R square = 3855.422/4918 = 0.783941
r =sqrt(0.783941) =0.8854
estimated slope is negative, therefore r is negative.
coefficient of correlation r = -0.8854
d) what is the percentage of the total variation in candy bar sales explained by the regression model?
R square = 3855.422/4918 = 0.783941
78.39% of the total variation in candy bar sales explained by the regression model.
e) if the price of the candy bar is set at $2, what is the predicted sales to be?
The regression line sales= 161.3855-48.1928*price
When price =2, predicted sales =161.3855-48.1928*2
=$64.9999
or
$65 ( rounded)
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