Least squares method to find regression coefficients

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Reference no: EM1319859

During the fall harvest season in the United States, pumpkins are sold in large quantities at farm stands. Often, instead of weighing the pumpkins prior to sale, the farm stand operator will just place the pumpkin in the appropriate circular cutout on the counter. When asked why this was done, one farmer replied, "I can tell the weight of the pumpkin from its circumference." To determine whether this was really true, a sample of 15 pumpkins were measured for circumference and weighed with the following results.

Circumference (CM)	Weight (Grams)
50	1200
55	2000
54	1500
52	1700
37	500
52	1000
53	1500
47	1400
51	1500
63	2500
33	500
66	2500
83	4600
60	2300
59	2100

1. Assuming a linear relationship, use the least squares method to find the regression coefficients b₀ and b₁.

2. Interpret the meaning of the slope b₁ in this problem.

3. Predict the average weight for a pumpkin that is 60 centimeters in circumference.

4. At the 0.05 level of significance, is there evidence of a linear relationship between the circumference and the weight of a pumpkin? Explain.

Reference no: EM1319859

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