Question

Temperature | # of ce coram coy יר 10 80 83 g0 as 13 12 19 23 105 S whneer the emperature increass a 1 dearce . // the expectd numlar ofic cromonestulIYncreasy ng how many cones

Answer 1

Let, x = temperature

y = # ice cream cones sold per hour

Let us fit a linear regression. The model would be,

$y_i = \beta_0 + \beta_1 x_i + \epsilon_i$ where, i = 1, 2, 3....

Now, the fitted model would be,

$\hat y_i =\hat \beta_0 +\hat \beta_1 x_i$

$\hat \beta_1 = \frac{S_{xy}}{S_{xx}} = \frac{11965 - 9 * 85 * 14.8889}{66525 - 9 * 85^2} = 0.3833$

$\hat \beta_0 = \bar y - \hat \beta_1 \bar x = 14.8889 - 0.3833 * 85 = -17.6944$

So the fitted model becomes,

$\hat y_i = -17.6944 + 0.3833x_i$

So, whenever temperature increases 1 unit, expected number of ice creams sold per hour increases by 0.3833 units

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